physics

PHYSICS 2PHYSICS 2

ELECTROMAGNETISELECTROMAGNETISMM

The study of electrical and The study of electrical and magnetism phenomena and the magnetism phenomena and the relationship between them.relationship between them.

History of History of ElectromagnetismElectromagnetism

Michael Faraday & James Clerk Michael Faraday & James Clerk MaxwellMaxwell They were further developedThey were further developed But, Maxwell expressed Faraday’s idea But, Maxwell expressed Faraday’s idea

as mathematical equations alongside his as mathematical equations alongside his own.own.

Hans Christian OestedHans Christian Oested Found-out that there is connection Found-out that there is connection

between electricity and magnetism between electricity and magnetism when he noticed that an electric current when he noticed that an electric current deflects a compass needle.deflects a compass needle.

Rubbing a piece of amber would Rubbing a piece of amber would enable it to attract bits of straw.enable it to attract bits of straw.

““This phenomenon is already This phenomenon is already known in ancient Greece.”known in ancient Greece.”

The world “Electron”, the The world “Electron”, the negatively charged subatomic negatively charged subatomic particles, came from the Greek particles, came from the Greek word which means “Amber”.word which means “Amber”.

History

Electric ChargeElectric Charge Like mass, is a fundamental Like mass, is a fundamental

property of certain of the property of certain of the elementary particles of which elementary particles of which all matter is composed.all matter is composed.

Fundamental physical quantity Fundamental physical quantity responsible for electric responsible for electric phenomena.phenomena.

Two kind of Electric chargeTwo kind of Electric charge

Positively charge Positively charge Negatively charge Negatively charge

Fundamental rule of all electric Fundamental rule of all electric phenomena:phenomena: Like charges it repels.Like charges it repels. Opposite charges it attracts.Opposite charges it attracts.

““This phenomena was discovered by Charles This phenomena was discovered by Charles Du Fay in 1733. The basic law of Du Fay in 1733. The basic law of Electrostatics.Electrostatics.

+ + + + + +

+ + + + + + + + + + + +

F

F

F

Repulsion

Attraction

F

Charged ParticlesCharged Particles Matter is made-up of atoms.Matter is made-up of atoms.

Each atom consist of Proton, Electron and Each atom consist of Proton, Electron and Neutron.Neutron.

Proton are particles with positive Proton are particles with positive charge.charge.

Electron are particles with negative Electron are particles with negative charge.charge.

Neutron are particles with no charge.Neutron are particles with no charge.

““Protons and Neutron are bound to form Protons and Neutron are bound to form the nucleus of the atom. Electron are the nucleus of the atom. Electron are mobile, moving around the nucleus and mobile, moving around the nucleus and can move from one nucleus to another.”can move from one nucleus to another.”

Quantization of chargeQuantization of charge Each Proton has a charge of +1.6x10Each Proton has a charge of +1.6x10-19-19CC Each Electron has a charge of -1.6x10Each Electron has a charge of -1.6x10--

1919CC The Unit of Charge is coulomb (C).The Unit of Charge is coulomb (C). The charge 1.6x10The charge 1.6x10-19-19C is denoted as e.C is denoted as e.

Hence, each proton has charge of +e and each Hence, each proton has charge of +e and each electron has charge of –e.electron has charge of –e.

Since the charge of all object ultimately Since the charge of all object ultimately depends on the number of Protons and depends on the number of Protons and Electrons, all charges are discrete values of e.Electrons, all charges are discrete values of e.

There can only be 1e, 2e, 3e . . . . There can only be 1e, 2e, 3e . . . . nne, but, it is e, but, it is not possible to have 0.5e or 0.125e.not possible to have 0.5e or 0.125e.

Q = Q = n n ee

Where:Where:

Q = Charge (Coulomb)Q = Charge (Coulomb)

nn = “quantity” Integer ( a = “quantity” Integer ( a complete entity or any of complete entity or any of the natural number with the natural number with + & -)+ & -)

e = (1.6 x 10e = (1.6 x 10-19-19C)C)

Sample problem:Sample problem:

How many electrons must be added How many electrons must be added to a neutrally charged body to give to a neutrally charged body to give a net charge of -1C?a net charge of -1C?

An object has a net positive charge An object has a net positive charge of 0.08 C if 1.5 x10of 0.08 C if 1.5 x101818 electron were electron were transferred to that object, How transferred to that object, How much is the new charge?much is the new charge?

CHARGINGCHARGING

There are different ways There are different ways of making an object of making an object

positively and negatively positively and negatively charged.charged.

Charging by FrictionCharging by Friction

It happens when one object It happens when one object rubbing with another object rubbing with another object allows the transfer of electrons allows the transfer of electrons from one to the other.from one to the other.

Charging by ContactCharging by Contact

It happens when electrons are It happens when electrons are transferred by simply touching transferred by simply touching one object with another.one object with another.

Charging by InductionCharging by Induction

It allows the movement of It allows the movement of charges within a conductor even charges within a conductor even without touching or rubbing it without touching or rubbing it with another object.with another object.

Electricity Electricity conductionconduction

Most substances conduct Most substances conduct electricity either very electricity either very well or very badly.well or very badly.

ConductorsConductors

InsulatorsInsulators

Semi-conductorsSemi-conductors

Super-conductorsSuper-conductors

Every materials can be Every materials can be classified accordingly:classified accordingly:

ConductorsConductors Through which charge can flow Through which charge can flow

easily from one substance to easily from one substance to another.another.

Has high electron mobility. Has high electron mobility.

(free electron flow)(free electron flow)

InsulatorsInsulators Materials that do not allow much Materials that do not allow much

movement of chargemovement of charge Has low electron mobility. Has low electron mobility.

(few or no free electron flow)(few or no free electron flow)

SemiconductorSemiconductor Materials that has varying Materials that has varying

conducting properties depending conducting properties depending on the impurities and the charges on the impurities and the charges present on the material.present on the material.

SuperconductorSuperconductor Materials that become perfect Materials that become perfect

conductors at extremely low conductors at extremely low temperature.temperature.

State that the Force between two State that the Force between two charges is proportional to the product charges is proportional to the product of the charges and is inversely of the charges and is inversely proportional to the square of the proportional to the square of the distance between them.distance between them.

221

r

qqkFe

COULOMB’ S LAWCOULOMB’ S LAW

Gave a quantitative description of the strength Gave a quantitative description of the strength of attraction and repulsion between charges.of attraction and repulsion between charges.

qq11 and q and q22 are the amount of charges in the are the amount of charges in the particles (in coulombs or C).particles (in coulombs or C).

r is the distance between two charged r is the distance between two charged particles (in meter).particles (in meter).

k is the proportionality constant = 9 x10k is the proportionality constant = 9 x1099 NmNm22/c/c22..

εε00 is a permeability constant = 8.854 x10 is a permeability constant = 8.854 x10-12-12 cc22/Nm/Nm22..

221

0221

4

1

r

qq

r

qqkFe

Sample Problem:Sample Problem:

A hydrogen atom is composed of A hydrogen atom is composed of an electron and a proton. The an electron and a proton. The Bhor radius of the hydrogen Bhor radius of the hydrogen atom is 5.30 x10atom is 5.30 x10-11-11 m. Compute m. Compute for the electrical force between for the electrical force between the proton and the electron in the proton and the electron in the atom.the atom.

Electrostatic Force (F)Electrostatic Force (F)

-+

F

r

Q1 Q2

Electrical & Static ForceElectrical & Static Force

BOHR RADIUSBOHR RADIUS

Notation of Electrostatic Notation of Electrostatic ForceForce

(Like charge repel, unlike charge attract.)(Like charge repel, unlike charge attract.)

+

-

+ -

-

+r

r

r

F F

F F

F F

Sample problem:Sample problem: Three point charges in a plane forming a right Three point charges in a plane forming a right

triangle, as shown figure below. Find the triangle, as shown figure below. Find the magnitude of electrostatic force acting on each magnitude of electrostatic force acting on each charge.charge.

+

+-

0.2 m

0.3 m

Q1= 1.0 nC

Q2= 3.0 nC

Q3= 2.0 nC

1.1. Find the electrostatic force between two Find the electrostatic force between two electrons 2 mm apart?electrons 2 mm apart?

2.2. Two identical charge of 4 Two identical charge of 4 µCµC each are 10 each are 10 mm apart. Find the Electrostatic force.mm apart. Find the Electrostatic force.

3.3. Two point charges QTwo point charges Q11 = 4 = 4µC, QµC, Q2 2 = 2µC = 2µC are 30 cm apart. are 30 cm apart.

4.4. Three point charges are along the same Three point charges are along the same line, as shown in the figure below. Find line, as shown in the figure below. Find the Electrostatic force between each the Electrostatic force between each charge.charge.

Problem solving:Problem solving:

Q1= +3µC Q1= -5µC Q1= +8µC

20 mm 35 mm

ELECTRIC ELECTRIC FIELDSFIELDS

Force at a DistanceForce at a Distance

Forces that one object can exert to Forces that one object can exert to another object with or without another object with or without physical contact between the physical contact between the objects.objects. Examples are Examples are GravityGravity and and

Electrostatic forceElectrostatic force.. Object with mass surrounded byObject with mass surrounded by

gravitational fieldgravitational field. . Object with Object with charge are surrounded by charge are surrounded by electric electric fieldfield..

Law of GravitationLaw of Gravitation

Gravitational fieldGravitational field

Equations:Equations: The equation of gravity:The equation of gravity:

Universal Law of GravitationUniversal Law of Gravitation

The equation of Electrostatic force:The equation of Electrostatic force: Coulomb’s LawCoulomb’s Law

221

r

mmGFg

221

r

QQkFe

Electric FieldElectric Field Field of force that surround a Field of force that surround a

charged object or particle.charged object or particle.

Force per unit Charge.Force per unit Charge.

It is denoted as E, and its It is denoted as E, and its unit is Newton per coulomb:unit is Newton per coulomb:

+

+ChargeElectric Fields

Where:Where: E = Electric fieldE = Electric field

Q = ChargeQ = Charge r = radius of the fieldr = radius of the field

k = proportionality k = proportionality constantconstant

2r

QkE

Electric field equationElectric field equation

Made of infinitely many electric field Made of infinitely many electric field vectors.vectors.

Electric of a positive charges directed Electric of a positive charges directed away from the charge.away from the charge.

The electric field of negative charge is The electric field of negative charge is directed toward the charge.directed toward the charge.

+Q -Q

PP

Drawing Electric Field Drawing Electric Field LinesLines

The lines must begin on positive The lines must begin on positive charges (or infinity)charges (or infinity)

The lines must end on negative The lines must end on negative charge (or infinity)charge (or infinity)

The number of lines leaving a The number of lines leaving a positive charge (or approaching positive charge (or approaching a negative charge) is a negative charge) is proportional to the magnitude of proportional to the magnitude of the charge.the charge.

ProportionalityProportionality

+ 2+


1. Find (a) the magnitude of an electrons 1. Find (a) the magnitude of an electrons electric field at 50.0 cm away from the electric field at 50.0 cm away from the electron. (b) if the another electron is electron. (b) if the another electron is placed at this distance, what would be the placed at this distance, what would be the magnitude of electrostatic force between magnitude of electrostatic force between the electrons? (c) Is the force attractive or the electrons? (c) Is the force attractive or repulsive?repulsive?

2. Two charges, Q2. Two charges, Q11 = +1.5 x 10 = +1.5 x 10-8-8 C and C and Q Q22 = +3.0 x 10 = +3.0 x 10-8-8 C are 100 mm apart. C are 100 mm apart. What is the magnitude of the electric field What is the magnitude of the electric field halfway between them?halfway between them?

GAUSS’ LAWGAUSS’ LAW A relation between the electric field at A relation between the electric field at

all the points on a closed surface and all the points on a closed surface and the total charge enclosed within the the total charge enclosed within the surface.surface.

Named after Karl Friedrich Gauss Named after Karl Friedrich Gauss (1777-1855(1777-1855

An alternative to Coulomb’s Law.An alternative to Coulomb’s Law.

Uses symmetry properties of given Uses symmetry properties of given charges to simplify electric field charges to simplify electric field calculations.calculations.

The strength of an electric field over an area The strength of an electric field over an area in field region.in field region.

Quantifies the notion “number of field lines Quantifies the notion “number of field lines crossing a surface”.crossing a surface”.

The dot product of electric field vector The dot product of electric field vector passing through the area and the area vector.passing through the area and the area vector.

Where:Where:

E = Electric fieldE = Electric field

A = Area of the surfaceA = Area of the surface

θθ = Angle of elevation of the surface = Angle of elevation of the surface

cosEAEA

Electric Flux (Electric Flux (ΦΦ))

GAUSS’ LAWGAUSS’ LAW

ΦΦ = EA cos 0 = EA cos 000

E

A


A

E


If the electric field in the region If the electric field in the region has a magnitude of 2.0 x 10has a magnitude of 2.0 x 1033 N/C N/C and passing through the surface and passing through the surface with an area 0.0214 mwith an area 0.0214 m22. The area . The area vector is oriented at an angle of vector is oriented at an angle of 505000 with respect to the electric with respect to the electric field. Find the electric flux.field. Find the electric flux.

Gaussian surfaceGaussian surface A hypothetical surface immersed in A hypothetical surface immersed in

electric field.electric field. It may or may not enclose a charge.It may or may not enclose a charge. Can be of any shape you wish to make Can be of any shape you wish to make

it, but the most useful surface is one it, but the most useful surface is one that mimics the symmetry of the that mimics the symmetry of the problem at hand.problem at hand.

The area vector is always the face The area vector is always the face outside the enclosed surface.outside the enclosed surface.

Net fluxNet flux Gauss’ Law in mathematical form:Gauss’ Law in mathematical form:

Where Where ΣΣqq enc enc is the total charge enclosed.is the total charge enclosed.

Any Gaussian surface that does not enclose Any Gaussian surface that does not enclose any charge has zero electric flux.any charge has zero electric flux.

If a Gaussian surface encloses a positive If a Gaussian surface encloses a positive charge (or positive sum of several enclosed charge (or positive sum of several enclosed charges), the electric flux is positive.charges), the electric flux is positive.

If a Gaussian surface encloses a negative If a Gaussian surface encloses a negative charge (or negative sum of several enclosed charge (or negative sum of several enclosed charges), the electric flux is negative.charges), the electric flux is negative.

0 encq

No enclosed charge(Zero flux)

Positive charge enclosed(Positive flux)

Negative charge enclosed(Negative flux)

Sample problem:Sample problem: Given five charges of values QGiven five charges of values Q1 1 = Q= Q55 = +3.1 = +3.1

nC, QnC, Q22 = Q = Q44 = -5.9 nC & q = -5.9 nC & q33 = +3.1 nC, find = +3.1 nC, find the net electric flux through the Gaussian the net electric flux through the Gaussian surface S shown in the figure below.surface S shown in the figure below.

-

-

-+

+

Q1

Q2

Q3

Q4

Q5

ELECTRIC POTENTIAL ELECTRIC POTENTIAL ENERGYENERGY

Potential energy due to the location of a Potential energy due to the location of a charge in an external electric field.charge in an external electric field.

If a charge If a charge QQ00 is within the electric field of is within the electric field of another charge another charge QQ, the potential of , the potential of QQ00 isis

Where Where r r is the distance of is the distance of QQ00 from from QQ..

r

QQkU e

0

Work done in Electric Work done in Electric FieldField

It is negative change in potential It is negative change in potential energy.energy.

If the charge moves between If the charge moves between two points with different electric two points with different electric field intensity.field intensity.

UW

Conclusion:Conclusion: When a positive/negative charge moves in When a positive/negative charge moves in

the direction of an electric field, the field the direction of an electric field, the field does positive/negative work and the does positive/negative work and the potential energy decreases.potential energy decreases.

When positive charge moves in the When positive charge moves in the direction opposite to an electric field, the direction opposite to an electric field, the field does negative work and the potential field does negative work and the potential energy increases.energy increases.

ELECTRIC POTENTIALELECTRIC POTENTIAL

Electric potential energy per unit Electric potential energy per unit charge arises due to location charge arises due to location within an electric field.within an electric field.

Related to electrostatic potential Related to electrostatic potential energy in the same way energy in the same way electrostatic force is related to electrostatic force is related to electric field.electric field.

For a point charge For a point charge QQ, the electric , the electric potential at point potential at point rr away from the away from the point charge is:point charge is:

If a test charge If a test charge QQ00 is placed in a region is placed in a region where the electric potential is where the electric potential is VV, the , the electric potential energy of the point electric potential energy of the point charge ischarge is

r

Q

r

QkV

04

VQU e 0

The unit is volts (v)The unit is volts (v)

1V = 1 J/C1V = 1 J/C

Also known as Also known as voltagevoltage..

SAMPLE PROBLEM:SAMPLE PROBLEM:

What is the electric potential What is the electric potential at a distance of 5.29 x 10at a distance of 5.29 x 10-11-11 m m from the proton? What is the from the proton? What is the potential energy of the potential energy of the electron and proton at this electron and proton at this separation?separation?

Electric Potential and Electric Potential and Electric FieldElectric Field

The relationship between electric The relationship between electric potential potential V V and electric fieldand electric field E E isis

Where Where rr is the distance from the is the distance from the charge of the point under charge of the point under consideration.consideration.

ErV


(a) Find the magnitude of a (a) Find the magnitude of a proton’s electric field at 50.0 cm proton’s electric field at 50.0 cm away from it. away from it.

(b) What is the electric potential at (b) What is the electric potential at this distance?this distance?

POTENTIAL DIFFERENCEPOTENTIAL DIFFERENCE Work done per unit Work done per unit

charge as a charge is charge as a charge is moved between two moved between two points in an electric points in an electric field.field.

If a test charge If a test charge QQ is is moved from point moved from point AA to to point point BB, the potential , the potential difference between difference between AA and and BB is: is:

Q

WV

Q

WVVV AB

Potential of the earth Potential of the earth arbitrarily said to be zero.arbitrarily said to be zero.

Ultimate responsible for the Ultimate responsible for the movement of charge and movement of charge and generation of electric current.generation of electric current.

Potential Difference Potential Difference ((∆V)∆V)

Can be either positive or negative with Can be either positive or negative with respect to the earth, depending on the respect to the earth, depending on the nature of the charge.nature of the charge.

WWABAB is positive the electric potential at is positive the electric potential at B B will will be higher than the electric potential at point be higher than the electric potential at point AA..

WWABAB is negative the electric potential at is negative the electric potential at BB will will be lower than the electric potential at point be lower than the electric potential at point AA..

WWABAB is zero the electric potential at is zero the electric potential at BB will be will be the same as the electric potential at point the same as the electric potential at point AA..


The work done on a 5.0 C The work done on a 5.0 C charge is 7.5 J as it is moved charge is 7.5 J as it is moved from point A, where the from point A, where the potential difference is 2.0 V, potential difference is 2.0 V, to another point B. What is to another point B. What is the electric potential the electric potential difference between points A difference between points A and points B? What is the and points B? What is the potential at point B?potential at point B?

POTENTIAL FOR MULTIPLE POTENTIAL FOR MULTIPLE CHARGESCHARGES

Calculate the separate potentials of each Calculate the separate potentials of each charge.charge.

Add the potentials with these signs Add the potentials with these signs corresponding to the sign of the charge.corresponding to the sign of the charge.

Where Where nn is the number of charges. is the number of charges.

n

n

n

r

Q

r

Q

r

Q

r

QkV

VVVVV

.........

.......

3

3

2

2

1

1

321


The three charges in with QThe three charges in with Q11= 8x10= 8x10-9-9C, C, QQ2 2 = 2.0x10= 2.0x10-9-9C and QC and Q3 3 = -4.0x10= -4.0x10-9-9C; are C; are separated by distance rseparated by distance r21 21 = 0.03m and = 0.03m and rr3131= 0.05m. Find:= 0.05m. Find: Potential due to QPotential due to Q22 at the point at the point

occupied by Qoccupied by Q11.. Potential due to QPotential due to Q33 at the point at the point

occupied by Qoccupied by Q11.. Net potential at point occupied by QNet potential at point occupied by Q11..

CAPACITORCAPACITOR

Also called condenserAlso called condenser A device to stores charge in the A device to stores charge in the

electric field between its plates.electric field between its plates. The plates carry charges of the The plates carry charges of the

same magnitude and opposite same magnitude and opposite sign.sign.

Ant two parallel conductors Ant two parallel conductors separated by an insulator (or separated by an insulator (or vacuum).vacuum).

Symbol:Symbol:

Example of capacitorExample of capacitor

Plates

CAPACITANCECAPACITANCE The ability of a capacitor is to store The ability of a capacitor is to store

energy.energy. The ratio of charge to potential The ratio of charge to potential

difference.difference. The unit is Farad (F) = coulomb/voltThe unit is Farad (F) = coulomb/volt Capacitance depends on:Capacitance depends on:

Area of the platesArea of the plates Distance between the platesDistance between the plates Nature of insulating materials Nature of insulating materials

(Dielectric)(Dielectric)

Space between the plates has Space between the plates has uniform electric field.uniform electric field.

The potential difference (The potential difference (V V ) voltage ) voltage between the plates between the plates aa and and bb is given is given by:by:

Where Where EE is the electric field and is the electric field and rr is is between platesbetween plates

ErVVV baab

Capacitance for parallel plates Capacitance for parallel plates capacitorscapacitors

The capacitance of a parallel plate The capacitance of a parallel plate capacitor:capacitor:

Where:Where: εε00 = permeability constant of the free space= permeability constant of the free space

= 8.85 x 10= 8.85 x 10-12-12 c c22/Nm/Nm22

= 8.85 x 10= 8.85 x 10-12-12 F/m F/m

A A = area of the plate= area of the plate

r r = distance between the plate = distance between the plate

r

A

V

QC

ab0

A larger area will have less repulsion A larger area will have less repulsion between charges.between charges.

A greater separation means lesser A greater separation means lesser charge is drawn and the capacitance charge is drawn and the capacitance is less.is less.

+ Q

- QA

r


The plates of a parallel-plate The plates of a parallel-plate capacitor are 5.00 mm apart and capacitor are 5.00 mm apart and 2.00 m2.00 m22 in area. A potential in area. A potential difference of 10,000 volts is difference of 10,000 volts is applied across the capacitor. applied across the capacitor. Compute the capacitance, the Compute the capacitance, the charge on the plate and the charge on the plate and the magnitude of the electric field in magnitude of the electric field in the space between them.the space between them.

DIELECTRICDIELECTRIC Insulating/non-conducting material between the Insulating/non-conducting material between the

plates of the capacitor.plates of the capacitor. Its function include:Its function include:

Solve the mechanical problem of maintaining Solve the mechanical problem of maintaining two plates at a very small separation w/o two plates at a very small separation w/o actual contact.actual contact.

Increased the maximum possible voltage Increased the maximum possible voltage between the two plates w/o experiencing a between the two plates w/o experiencing a “dielectric breakdown”.“dielectric breakdown”.

Dielectric breakdown happens when the Dielectric breakdown happens when the dielectric materials becomes slightly dielectric materials becomes slightly conducting.conducting.

Increase capacitance.Increase capacitance.

Dielectric ConstantDielectric Constant Ratio between the capacitance of a Ratio between the capacitance of a

capacitor when a dielectric material capacitor when a dielectric material is present (is present (CC) and its capacitance ) and its capacitance when the space between its plate is when the space between its plate is a vacuum (a vacuum (CC00))

oC

Ck

Where:Where:

kk = dielectric constant= dielectric constant

CC = Capacitance if there is = Capacitance if there is dielectricdielectric

CC00 = capacitance without = capacitance without dielectricdielectric

Ratio of the permittivity of the dielectric Ratio of the permittivity of the dielectric and the permittivity in a vacuum.and the permittivity in a vacuum.

Always greater the 1 because C>CAlways greater the 1 because C>C00, , when the charge on the plate is when the charge on the plate is constant. It is also unitless.constant. It is also unitless.

Where:Where:

kk = dielectric constant= dielectric constant

εε = Capacitance if there is = Capacitance if there is dielectricdielectric

εε00 = capacitance without = capacitance without dielectricdielectric

= 8.85 x 10= 8.85 x 10-12-12 C C22/Nm/Nm22

o

k

Dielectric Materials

PLATE

PLATE

+

-

Sample problem:Sample problem: The parallel plates of a capacitor have an area of The parallel plates of a capacitor have an area of

2.00 x 102.00 x 10-1-1 m m22 and have a separation distance of and have a separation distance of 1.00 x 101.00 x 10-2-2 m and are connected to 3000 volts m and are connected to 3000 volts power supply.power supply.The capacitor is then disconnected from the The capacitor is then disconnected from the supply, and an dielectric is inserted between the supply, and an dielectric is inserted between the plates, Find that the potential difference decreases plates, Find that the potential difference decreases to 1000 volts while the charge on each plate to 1000 volts while the charge on each plate remain constant.remain constant.Find the following:Find the following:

a) Original capacitance (C),a) Original capacitance (C),b) magnitude of charge on each plate,b) magnitude of charge on each plate,c) capacitance, C after dielectric is inserted,c) capacitance, C after dielectric is inserted,d) the dielectric constant k of the dielectricd) the dielectric constant k of the dielectrice) permittivity of the dielectrice) permittivity of the dielectric

EQUIVALENT EQUIVALENT CAPACITANCECAPACITANCE

Capacitance of the single Capacitance of the single capacitor that can replace a set of capacitor that can replace a set of interconnected capacitors.interconnected capacitors.

CT

VT

C1 C3C2

VT

Capacitors in Series Capacitors in Series ConnectionConnection

The end of the capacitor is The end of the capacitor is connected to the end of the connected to the end of the adjacent capacitor.adjacent capacitor.

C1 C3C2

VT

The relationship of individual The relationship of individual capacitances, charges and voltage to capacitances, charges and voltage to equivalent capacitance, charge and equivalent capacitance, charge and voltage respectively are as follow:voltage respectively are as follow:

nT

nT

nT

CCCCC

VVVVV

QQQQQ

1......

1111

......

......

321

321

321

Capacitors in Parallel Capacitors in Parallel connectionconnection

Each has one end joined to the Each has one end joined to the corresponding end of all the corresponding end of all the other capacitors.other capacitors.

C1 C2 C3

VT

nT

nT

nT

CCCCC

VVVVV

QQQQQ

......

......

......

321

321

321

The relationship of individual The relationship of individual capacitances, charges and voltage capacitances, charges and voltage to equivalent capacitance, charge to equivalent capacitance, charge and voltage respectively are as and voltage respectively are as follow:follow:


1.1. Two capacitors one is 491 Two capacitors one is 491 µF and the other µF and the other is 30 µF are connected in series across a 12 is 30 µF are connected in series across a 12 volts battery. Find the equivalent volts battery. Find the equivalent capacitance of the combination, the charge capacitance of the combination, the charge on each capacitor and the potential on each capacitor and the potential difference across it.difference across it.

2.2. Two capacitor one is 5 F and the other 2 F Two capacitor one is 5 F and the other 2 F are connected in parallel across a 100 volts are connected in parallel across a 100 volts battery. Find the equivalent capacitance of battery. Find the equivalent capacitance of the combination, the charge of each and the the combination, the charge of each and the potential difference on each capacitor.potential difference on each capacitor.

What is the equivalent capacitance of What is the equivalent capacitance of the mixed series and parallel the mixed series and parallel capacitors shown below?capacitors shown below?

5mF

4mF18mF

ELECTRIC ELECTRIC CURRENTCURRENT

A flow of charge from one place A flow of charge from one place to another. The unit is to another. The unit is AmpereAmpere, ,

which equal to a flow of 1 which equal to a flow of 1 coulomb per second.coulomb per second.

Moving charges as a Moving charges as a currentcurrent

Its described as a stream of Its described as a stream of moving charges.moving charges.

May range very small currents May range very small currents such as the nerve impulses to a such as the nerve impulses to a large as the solar wind emitted large as the solar wind emitted by the sun.by the sun.

There must be a “net” flow of There must be a “net” flow of charges towards one direction.charges towards one direction.

When moving charges is not a When moving charges is not a currentcurrent

When there is no net flow of When there is no net flow of charge even though there are charge even though there are actual movement.actual movement.

Example:Example: Electrons of a copper conductor in Electrons of a copper conductor in

absence of electric potential.absence of electric potential. Electrons just move randomly the Electrons just move randomly the

charge flowing charge flowing to charge flowing charge flowing to one direction is equal to those one direction is equal to those flowing to the other direction. flowing to the other direction.

Electric current in a Electric current in a conductorconductor

An isolated conductor in absence of An isolated conductor in absence of electric potential contains free flowing electric potential contains free flowing electrons but no electric current.electrons but no electric current.

Isolated conducto

r

charges

A conductor connected to a dry cell or A conductor connected to a dry cell or battery has the necessary electric potential battery has the necessary electric potential to influence the flow of charges towards to influence the flow of charges towards one direction, hence producing current.one direction, hence producing current.

Battery

+ -

Conductor

Charges

Direction of charges

Electric current (Electric current (I I ) is defined as the ) is defined as the amount of charges passing through a amount of charges passing through a hypothetical plane intersecting the hypothetical plane intersecting the conductor per unit of time.conductor per unit of time.

Its unit is coulomb per second (C/s), also Its unit is coulomb per second (C/s), also called ampere (A).called ampere (A).

t

QI

Where:Where:

I = Current (ampere, I = Current (ampere, A)A)

Q = Charge (coulomb, c)Q = Charge (coulomb, c)

t = Time (second, s)t = Time (second, s)

-

-

-

-

-

-

t = t0 t = t0 + 1 s

plane plane

Independent to the selection of Independent to the selection of hypothetical planehypothetical plane

a b c

a’ b’

c’

I I


A wire carries a current of 0.8 A wire carries a current of 0.8 ampere. How many electrons ampere. How many electrons passes every section of the passes every section of the wire every one second?wire every one second?

Current is a scalar Current is a scalar quantityquantity

Electric current is moving along Electric current is moving along a conductor has only two a conductor has only two possible directions.possible directions.

Electric current are scalars. Electric current are scalars. Adding and Subtracting the Adding and Subtracting the current does not consider the current does not consider the orientation of the conductor in orientation of the conductor in space.space.

I0

I1

I2

I0 = I1 + I2

DIRECTION OF CURRENTDIRECTION OF CURRENT In reality, electric current are In reality, electric current are

movement of electrons along the movement of electrons along the conductor.conductor.

For historical reason, current is For historical reason, current is treated as flow of positive treated as flow of positive charges to the direction opposite charges to the direction opposite that of the actual movement of that of the actual movement of electrons.electrons.

These positive charges are not These positive charges are not actual particles. They are called actual particles. They are called holesholes, vacant spaces where , vacant spaces where there should be an electron. The there should be an electron. The charge of a hole is charge of a hole is +1.6 x 10+1.6 x 10-19 -19 CC..

Electrons are known as Electrons are known as negative negative charge carrierscharge carriers. Holes are known . Holes are known as as positive charge carrierspositive charge carriers..

Drift SpeedDrift Speed The net motion of charged particles as a group:The net motion of charged particles as a group:

Avqnt

QI d//

Where:Where:

I = electric current (A)I = electric current (A)

n = charge concentrationn = charge concentration

vvd d = drift velocity (m/s)= drift velocity (m/s)

e = charge of electrone = charge of electron

A = cross-sectional area A = cross-sectional area of conductor(mof conductor(m22))

Usually very small (10Usually very small (10-5 -5 or 10or 10-4-4 m/s) m/s) compared to random motion of compared to random motion of charges (10charges (10-6 -6 m/s)m/s)

Iin IinA

Current DensityCurrent Density

Current per unit of cross-sectional Current per unit of cross-sectional area of a conductor.area of a conductor.

A vector quantity with the same A vector quantity with the same direction as the motion of positive direction as the motion of positive charge carriers.charge carriers.

dvenA

IJ //

Where:Where:

II = electric current (A) = electric current (A)

JJ = current density (A/m = current density (A/m22))

n = charge concentrationn = charge concentration

vvd d = drift velocity (m/s)= drift velocity (m/s)

e = charge of electrone = charge of electron

A = cross-sectional area A = cross-sectional area of conductor(mof conductor(m22))


A 491 gauge copper wire has a A 491 gauge copper wire has a nominal diameter of 0.64 mm. nominal diameter of 0.64 mm. This wire carries a constant This wire carries a constant current of 1.67 A to a 4,910 watts current of 1.67 A to a 4,910 watts lamp. The density of free electron lamp. The density of free electron is 8.5 x 10is 8.5 x 102828 electrons/m electrons/m33. Find the . Find the current density and the current density and the magnitude of drift velocity.magnitude of drift velocity.

Types of CurrentTypes of Current

Direct currentDirect current The direction of current is constant.The direction of current is constant. The graph of current vs time is a The graph of current vs time is a

straight line.straight line. Developed by Developed by Tomas Alva EdisonTomas Alva Edison

Soon replaced by alternating current as Soon replaced by alternating current as primary means of transmitting primary means of transmitting electricity, but still used in battery electricity, but still used in battery operated devices.operated devices.

Alternating CurrentAlternating Current The direction and magnitude of the current The direction and magnitude of the current

continuously changes between two extremes.continuously changes between two extremes. The graph of current vs time is sinosoid.The graph of current vs time is sinosoid. Developed by Developed by Nikola TeslaNikola Tesla and and George George

WestinghouseWestinghouse, forming rivalry with , forming rivalry with

Thomas EdisonThomas Edison on on War of the War of the CurrentsCurrents..

The most commonly used method of electric The most commonly used method of electric transmission today.transmission today.

Direct CurrentDirect Current Alternating CurrentAlternating Current

I (A)

t (s)

I (A)

t (s)

ELECTRIC ELECTRIC RESISTANCERESISTANCE

Electric ResistanceElectric Resistance

Property of the conducting medium that Property of the conducting medium that weakens the transmission of electric weakens the transmission of electric current.current.

Denoted as Denoted as RR and its unit is and its unit is Ohm Ohm ((ΩΩ))..

A

LR

Where:Where:

R = Resistance (Ohm, R = Resistance (Ohm, ΩΩ))

ρρ = resistivity ( = resistivity (ΩΩm)m)

LL = Length of the wire = Length of the wire (m)(m)

A = cross-sectional A = cross-sectional area area of a wire(mof a wire(m22))

Approximate resistivities (at 200C)

and their temperature coefficient.

Substance ρ(Ω.m) α(k-1)

Aluminum 2.6 x 10-8 0.0039

Copper 1.7 x 10-8 0.0039

Iron 12 x 10-8 0.005

Lead 21 x 10-8 0.0043

Mercury 98 x 10-8 0.00088

Platinum 11 x 10-8 0.0036

Silver 1.6 x 10-8 0.0038


A piece of 1.0 m wire has a A piece of 1.0 m wire has a resistance of 0.19 ohms. Calculate resistance of 0.19 ohms. Calculate the resistivity of the wire. The the resistivity of the wire. The cross-sectional area of the wire is cross-sectional area of the wire is 0.5 mm0.5 mm22..

ρ

L

A

Resistivity & Resistivity & ConductivityConductivity

Resistivity (Resistivity (ρρ)) Measure of how much resistance a Measure of how much resistance a

material possesses against electric material possesses against electric current.current.

Intrinsic property of a material that Intrinsic property of a material that depends on its electronic structure.depends on its electronic structure.

Conducting material Electric field

Measure by placing the material Measure by placing the material between two plates with constant between two plates with constant electric field (electric field (EE ) and taking the ratio of ) and taking the ratio of electric field and current density (electric field and current density (JJ ))..

J

E

Varies with temperatureVaries with temperature

Where:Where:

ρρ = resistivity (= resistivity (ΩΩm)m)

E E = electric field (N/c)= electric field (N/c)

J J = current density = current density (A/m(A/m22))

ConductivityConductivity Measure of how the material is Measure of how the material is

capable of conducting electricity.capable of conducting electricity. Reciprocal of resistivity.Reciprocal of resistivity.

Variation of Resistivity Variation of Resistivity with Temperaturewith Temperature

Over a wide range of temperature, the graph of Over a wide range of temperature, the graph of resistivity vs temperature of metal is linear.resistivity vs temperature of metal is linear.

4002000 1200 1400

2

8

0

4

6

10

600 800 1000

Resis

tivit

y 1

0-8 Ω

m

Room

tem

pera

ture

Temperature (Kelvin)

Variation of Resistivity Variation of Resistivity with Temperaturewith Temperature

Thus it can be represented by a Thus it can be represented by a Linear equation.Linear equation.

000 TT Where:Where:

ρρ = resistivity ( = resistivity (ΩΩm)m)

ρρ0 0 = resistivity at room temperature ( = resistivity at room temperature (ΩΩm)m)

T = temperature (Kelvin,K)T = temperature (Kelvin,K)

TT0 0 = room temperature (K)= room temperature (K)

αα = coefficient of resistivity (K = coefficient of resistivity (K-1-1))

The The Temperature coefficient Temperature coefficient of resistivity (of resistivity (αα)) determines determines how much resistivity how much resistivity increases with temperature.increases with temperature.

Its unit is (per Kelvin)KIts unit is (per Kelvin)K-1-1..


What is the resistivity of iron at What is the resistivity of iron at 200K? Use the values of 200K? Use the values of resistivity (at room temperature) resistivity (at room temperature) and temperature coefficient of and temperature coefficient of the resistivity in the handout.the resistivity in the handout.

Ohm’s LawOhm’s Law

The current The current II (Ampere, A) is directly (Ampere, A) is directly proportional to the potential difference proportional to the potential difference VV (Volt,V) with resistance (Volt,V) with resistance RR (ohms, (ohms,ΩΩ) as ) as the proportionality constant.the proportionality constant.

IRV

Assumed that the resistance does Assumed that the resistance does not vary with voltage or current.not vary with voltage or current.

Not all conducting material follow Not all conducting material follow “Ohm’s Law”. Those are follow are “Ohm’s Law”. Those are follow are said to be said to be ohmicohmic , while those that , while those that do not are said to be do not are said to be non ohmicnon ohmic..

Current Potential Difference graph Current Potential Difference graph of a of a 1000 W resistor1000 W resistor, an , an OhmicOhmic device.device.

-4 -2 0 +2 +4

-2

+2

0Current (mA)

Potential Difference (V)

Current vs Potential Difference Current vs Potential Difference graph of a graph of a pn junction diodepn junction diode, a , a

non-ohmicnon-ohmic device. device.

-4 -2 0 +2 +4

-2

+2

0Current (mA)

Potential Difference (V)

Single Loop CircuitSingle Loop Circuit CircuitCircuit

Close network of electronic devices Close network of electronic devices through which current constantly flows.through which current constantly flows.

EMF DeviceEMF Device

Maintain potential difference.Maintain potential difference.

Provides steady flow of charge.Provides steady flow of charge.

EMF stand for EMF stand for Electromotive Electromotive forceforce..

R

EMF

I

+ -

+ -

I

The ResistorThe Resistor

Provides a resistance to the circuit.Provides a resistance to the circuit. It was specially designed to only It was specially designed to only

provide certain amount of resistance.provide certain amount of resistance. An Ohmic deviceAn Ohmic device

Such conductor device.Such conductor device. It was verified experimentally by the It was verified experimentally by the

German physicist German physicist Georg OhmGeorg Ohm (1787- (1787-1854).1854).

Electromotive ForceElectromotive Force A circuit consists of electrons from the A circuit consists of electrons from the

negative terminal of a battery to the negative terminal of a battery to the positive terminal of the battery.positive terminal of the battery.

Electrons must then return to the negative Electrons must then return to the negative terminal, or current will stop flowing.terminal, or current will stop flowing.

The electron are forced into this higher The electron are forced into this higher potential by a electromotive force.potential by a electromotive force.

EMF

EMF Devices:EMF Devices:

Battery or Dry CellBattery or Dry Cell

Electrochemical CellElectrochemical Cell

Electric GeneratorElectric Generator

Photovoltaic CellPhotovoltaic Cell

Internal ResistanceInternal Resistance The resistance found inside real The resistance found inside real

batteriesbatteries Lessen the output voltage of the battery.Lessen the output voltage of the battery. Denoted as Denoted as rrii

Its Its SISI unit is unit is Ohms (Ω)Ohms (Ω).. A real battery is now drawn as:A real battery is now drawn as:

EMF

ri

Terminal Potential Difference (Terminal Potential Difference (TPDTPD))

The output voltage of a source of The output voltage of a source of emfemf after internal resistance takes effect.after internal resistance takes effect.

The equation used to solve for terminal The equation used to solve for terminal potential difference is:potential difference is:

TPD = E – IrTPD = E – Irii Where:Where:

TPDTPD = voltage across the source (V)= voltage across the source (V)

E E = voltage if the source is ideal = voltage if the source is ideal emf emf (V)(V)

rrii = internal resistance of the source (Ω)= internal resistance of the source (Ω)

II = current flowing through the battery (A)= current flowing through the battery (A)

A 6.0 V battery is connected to an A 6.0 V battery is connected to an external 6.0 0hms resistor.external 6.0 0hms resistor.

(a)(a) What is the value of the current What is the value of the current flowing through the external flowing through the external circuit if there is no internal circuit if there is no internal resistance,resistance,

(b)(b) What is the value of the current What is the value of the current flowing through the external flowing through the external circuit when the internal circuit when the internal resistance is 0.3 ohms?resistance is 0.3 ohms?


Resistors in Single Resistors in Single Loop CircuitLoop Circuit

Where: R is resistance, I is electric current and V is Where: R is resistance, I is electric current and V is electric potential difference.electric potential difference.

R3

VT

IT+ -

+

R2

+

R1

+ - --

RT

Resistors in Series Resistors in Series Circuit.Circuit.

Equivalent resistance in a Equivalent resistance in a Series CircuitSeries Circuit

nT

nT

nT

VVVVV

IIIII

RRRRR

.........

........

.......

321

321

321


Resistors RResistors R11 = 2.00 ohms, R = 2.00 ohms, R22 = = 3.00 ohms and R3.00 ohms and R33 = 4.00 ohms are = 4.00 ohms are in series connection with a in series connection with a voltage source of 100.0 volts. voltage source of 100.0 volts. Find the equivalent resistance, Find the equivalent resistance, electric current and electric electric current and electric potential difference.potential difference.

Resistor in Parallel CircuitResistor in Parallel Circuit

R3

VT

IT+ -

+

R2+

R1+ -

-

-RT

I3

I2

I1

Equivalent resistance in Equivalent resistance in a Parallel Circuita Parallel Circuit

nT

nT

nT

VVVVV

IIIII

RRRRR

.........

........

1.......

1111

321

321

321


Resistors RResistors R11 = 3.00 ohms, R = 3.00 ohms, R22 = = 5.00 ohms and R5.00 ohms and R33 = 7.00 ohms are = 7.00 ohms are in parallel connection with a in parallel connection with a voltage source of 110.0 volts. voltage source of 110.0 volts. Find the equivalent resistance, Find the equivalent resistance, electric current and electric electric current and electric potential difference.potential difference.

Resistors in Single Loop Resistors in Single Loop CircuitCircuit

Resistor in Series-Parallel CircuitResistor in Series-Parallel Circuit

R3

VT

IT

+ -

+

R2

+

R1

+ --

-

RT

POWER IN POWER IN CIRCUITSCIRCUITS

The Power in the CircuitsThe Power in the Circuits

Flow of current across a circuit.Flow of current across a circuit.

Movement of a charge across a Movement of a charge across a electric device:electric device: It moves from higher potential to It moves from higher potential to

lower potential.lower potential. Hence, there is a decrease in potential Hence, there is a decrease in potential

energy.energy.

Q

If there is a decrease in potential If there is a decrease in potential energy, there must be a energy, there must be a transmission to another form of transmission to another form of energy.energy.

Light bulb: to heat and light.Light bulb: to heat and light. Electric motor: to mechanical energyElectric motor: to mechanical energy Resistor: Internal energy/heat.Resistor: Internal energy/heat.

The rate at The rate at which electric which electric potential potential energy is energy is transformed to transformed to another form of another form of energy is the energy is the POWERPOWER in the in the circuit.circuit. R

VP

RIP

IRP

2

2

Sample Problem:

A current flowing through a A current flowing through a 25.0 ohm resistor is 2.0 A. 25.0 ohm resistor is 2.0 A. How much power is dissipated How much power is dissipated by the resistor.by the resistor.

MULTILOOP MULTILOOP CIRCUITCIRCUIT

Provides multiple paths for current.Provides multiple paths for current. When one component was cut-off, When one component was cut-off,

others can still function.others can still function.

What happen when one component in What happen when one component in a series circuit was cut-off?a series circuit was cut-off?

What happen when one component in What happen when one component in a multiloop circuit was cut-off?a multiloop circuit was cut-off?

Current in a Multiloop CircuitCurrent in a Multiloop Circuit The point where three or more The point where three or more

segments of the conductor meet is segments of the conductor meet is called the junction.called the junction.

The current split at the junction.The current split at the junction.

Junction

current

GUSTAV KIRCHHOFFGUSTAV KIRCHHOFF German physicist who, in the German physicist who, in the

collaboration with Robert William collaboration with Robert William Bunsen, develop ed the science of Bunsen, develop ed the science of spectrum analysis.spectrum analysis.

He showed that each element, when He showed that each element, when heated to incandescence.heated to incandescence.

He produced a characteristic pattern of He produced a characteristic pattern of emission lines.emission lines.

He formulated Kirchhoff’s Law for He formulated Kirchhoff’s Law for electric circuit.electric circuit.

(1824-1887)(1824-1887)

In any closed circuit, the algebraic sum of all In any closed circuit, the algebraic sum of all EMF’s and potential drop is equal to zero. EMF’s and potential drop is equal to zero. (Using loop direction)(Using loop direction)

KIRCHHOFF’S LAWKIRCHHOFF’S LAW

R2+

Emf1

+

-

R1

+

Emf2

+

-

R3

+

Loop 1 Loop 2

I1 I2I3

-

At any point in a circuit, the sum of the At any point in a circuit, the sum of the currents leaving the junction point is currents leaving the junction point is equal to the sum of all the current equal to the sum of all the current entering the junction point. (Using entering the junction point. (Using current direction).current direction).

R2+

ε1

+

-

R1

+

ε2

+

-

R3

Junction point

I1

I3

I2

+

Sample Problem:Sample Problem: In a given circuit below, Find: a) IIn a given circuit below, Find: a) I11, b) I, b) I22 and c) I and c) I33

10 Ω+

9v

+

-

15 Ω+

12v

+

-

5 Ω

I1

I3

I2

+

RC CIRCUITRC CIRCUIT(Resistor and Capacitor in a (Resistor and Capacitor in a

circuit)circuit)

Resistor- Capacitor in a circuit.Resistor- Capacitor in a circuit.

R

+ -

C

S1

S2

ε+

-

Where: Where: εε = Batteries (Emf)= Batteries (Emf)

SS11 & S & S22 = Switches = Switches

R = ResistorR = Resistor

C = CapacitorC = Capacitor

Open

Close

Charging a capacitorCharging a capacitor

CR VV

R

+ -

C

S1

S2

ε+

-

II

I

I I

closed

open

Where:VR = Potential difference across the resistor.VC = Potential difference across the capacitor.

I

Current Current IIOO at the moment S at the moment S11 closed ( closed (tt = 0) = 0)

Current Current I I at any time at any time tt after S after S11 closed: closed:

After some time After some time tt The charge of the capacitor (q) increasesThe charge of the capacitor (q) increases Current (Current (II ) decreases. ) decreases.

RI

0

RC

q

RI

Until the capacitor reaches its Until the capacitor reaches its equilibrium chargeequilibrium charge (q (qeqeq), happen ), happen when Vwhen VCC reaches V reaches VCC = = εε, which , which result to result to II = 0 = 0

Cq

RC

q

R eq

Charge and current of the capacitor Charge and current of the capacitor at any given time at any given time tt after after tt = 0. = 0.

RC

t

RC

t

eCq

eR

I

1

The time constant (The time constant (ττ) of RC series ) of RC series circuit.circuit.

The unit of time constant is second. The unit of time constant is second. At timeAt time tt = = ττ

Q = 0.63 CQ = 0.63 Cεε II = 0.37= 0.37 IIoo

The charging time of RC circuits are The charging time of RC circuits are often stated in terms of time constant.often stated in terms of time constant.

Sample Problem:Sample Problem:A resistor with resistance R=1.0 x A resistor with resistance R=1.0 x 101066ΩΩ, capacitor with capacitance , capacitor with capacitance C=2.2 x 10C=2.2 x 10-6-6F, a voltage source with F, a voltage source with εε = 100 v, and a switch are all = 100 v, and a switch are all connected in a single loop series connected in a single loop series circuit. The switch is initially open. circuit. The switch is initially open. When the switch is closed, calculate:When the switch is closed, calculate:

(a)(a) Initial current across the resistorInitial current across the resistor

(b)(b) Equilibrium charge of the capacitorEquilibrium charge of the capacitor

(c)(c) Time constant of the circuitTime constant of the circuit

(d)(d) Current through the resistor after 5 secondsCurrent through the resistor after 5 seconds

(e)(e) Charge of the capacitor after 5 secondCharge of the capacitor after 5 second

(f)(f) Charge of the capacitor at t = Charge of the capacitor at t = ττ

MAGNETISMMAGNETISM

Introduction to MagnetismIntroduction to Magnetism

The first known magnet are the stoned exposed The first known magnet are the stoned exposed to earth’s magnetic field called to earth’s magnetic field called LoadstonesLoadstones, , discovered by early Greeks and Chinese.discovered by early Greeks and Chinese.

Magnet are surrounded by a field of force Magnet are surrounded by a field of force called called magnetic fieldmagnetic field..

The magnetic force, force exerted by magnets The magnetic force, force exerted by magnets to magnetic materials is a force at distance, to magnetic materials is a force at distance, just like gravity and electric force.just like gravity and electric force.

One of the earliest applications of magnetism is One of the earliest applications of magnetism is the magnetic compass.the magnetic compass.

Diskette, ATM cards and some other storage Diskette, ATM cards and some other storage device contain tiny bits of magnetic materials. device contain tiny bits of magnetic materials. Exposure to magnetic field would damage Exposure to magnetic field would damage these devices.these devices.

Magnetic field of magnetsMagnetic field of magnets The magnetic of a magnet has the greatest The magnetic of a magnet has the greatest

concentration on its two ends called concentration on its two ends called polespoles.. Magnetic field line are drawn to be emanating from theMagnetic field line are drawn to be emanating from the

north north polepole and terminates to the and terminates to the south polesouth pole..

N

S

N S N

S

Bar Magnet

HorseshoeMagnet

C-shapedMagnet

The magnetic field lines is made The magnetic field lines is made up of infinite number of up of infinite number of magnetic field vectors. Magnetic magnetic field vectors. Magnetic field vectors are drawn tangent field vectors are drawn tangent to the magnetic field line.to the magnetic field line.

This method of visualizing This method of visualizing magnetic fields was proposed by magnetic fields was proposed by Michael FaradayMichael Faraday, who initially , who initially called magnetic field called magnetic field lines of lines of forceforce or or line of inductionline of induction..

N S

Magnetic field

Magnetic field

Rules in drawing magnetic Rules in drawing magnetic field linesfield lines

The direction of the tangent to a magnetic The direction of the tangent to a magnetic field line at any point gives the direction of field line at any point gives the direction of the magnetic field vector at that point.the magnetic field vector at that point.

The spacing between the lines represents The spacing between the lines represents the magnitude of the magnetic field.the magnitude of the magnetic field.

Magnetic field lines emanate from the Magnetic field lines emanate from the north pole and terminate at the south north pole and terminate at the south pole.pole.

Polarity of MagnetPolarity of Magnet

Similar poles repel and opposite pole Similar poles repel and opposite pole attracts.attracts.

When a magnet is divided into two When a magnet is divided into two (or several parts), each part has its (or several parts), each part has its own north and south poles.own north and south poles.

As far as the current theories of As far as the current theories of magnetism are concerned, there are magnetism are concerned, there are no magnetic monopoles.no magnetic monopoles.

N N

N

S S

S

N N

N

S S

S

REPULSION

REPULSION

ATTRACTION

Definition of Magnetic Definition of Magnetic FieldField

Magnetic field is defined in terms of force Magnetic field is defined in terms of force it can exert on a charge particle, called it can exert on a charge particle, called magnetic force.magnetic force.

Magnetic force is a cross-product:Magnetic force is a cross-product:

qvF Where:F = Magnetic force (Newton)q = charge (coulomb)v = velocity (m/s)β = Magnetic field (Tesla)

The magnitude of the magnetic force is:The magnitude of the magnetic force is:

The direction of the magnetic force can The direction of the magnetic force can be determined using the be determined using the right-hand right-hand rulerule..

sinqvF

Where:θ is the angle between velocity and magnetic field.

Right-hand-rule:Right-hand-rule: Long, straight Current:Long, straight Current:

Grasp the wire with your right hand so that Grasp the wire with your right hand so that your thumb point in the direction of the your thumb point in the direction of the current. The curled fingers of that hand current. The curled fingers of that hand point the direction of the magnetic field.point the direction of the magnetic field.

Current loop:Current loop: Grasp the loop so that the curled fingers of Grasp the loop so that the curled fingers of

your hand point in the direction of the your hand point in the direction of the current; the thumb of that hand then point current; the thumb of that hand then point in the direction of the magnetic field.in the direction of the magnetic field.

Magnetic force can only change Magnetic force can only change the direction of the particle’s the direction of the particle’s motion, not its sound.motion, not its sound.

1 T = 1 kg/C-s1 T = 1 kg/C-s The SI unit of magnetic field (The SI unit of magnetic field (ββ) )

is Tesla (T).is Tesla (T). A non-SI unit called gauss (G) is A non-SI unit called gauss (G) is

also used.also used. 101044 G = 1 T G = 1 T


The velocity of an electron in a The velocity of an electron in a magnetic field of 2T is 4 x 10magnetic field of 2T is 4 x 1055m/s m/s perpendicular to the field. Find perpendicular to the field. Find the force that acts on the the force that acts on the charge.charge.

Magnetic ForceMagnetic Force

Magnetic force on a currentMagnetic force on a current Since current, by definition are moving Since current, by definition are moving

charge, current carrying conductors can charge, current carrying conductors can also be moved by magnetic field.also be moved by magnetic field.

The magnetic force for a straight The magnetic force for a straight conductor in a uniform electric field.conductor in a uniform electric field.

ILF Where:F = magnetic force (Newton)I = current (ampere)L = Length of the conductor inside the magnetic field (meter)β = Magnetic field (Tesla)

sinILF

The direction of the magnetic force The direction of the magnetic force is determined by right-hand-rule.is determined by right-hand-rule.

The magnitude of magnetic force is:The magnitude of magnetic force is:

Where:θ = is the angle between the wire and the magnetic field.


A wire 0.10 m long carrying a current A wire 0.10 m long carrying a current of 2.0 A is at 30of 2.0 A is at 3000 angle with respect angle with respect to the magnetic field. If the magnetic to the magnetic field. If the magnetic field strength is 0.20 T, what is the field strength is 0.20 T, what is the magnitude of the force on the wire?magnitude of the force on the wire?

Magnetic field of EarthMagnetic field of Earth Magnetic north pole is located Magnetic north pole is located

somewhere in the Greenland, near but somewhere in the Greenland, near but not exactly in the same location as not exactly in the same location as geographic north pole. Magnetic south geographic north pole. Magnetic south pole is at its direct opposite.pole is at its direct opposite.

Earth is the giant magnet that Earth is the giant magnet that generates magnetic field. It enables generates magnetic field. It enables compasses to work.compasses to work.

Earth magnetic north pole is actually Earth magnetic north pole is actually the “south pole”, where magnetic field the “south pole”, where magnetic field terminates, and the magnetic south terminates, and the magnetic south pole is actually the “north pole” from pole is actually the “north pole” from where the magnetic field emanates.where the magnetic field emanates.

Compasses:Compasses: Instrument used to find direction.Instrument used to find direction. Composed of slender bar magnet or Composed of slender bar magnet or

low friction pivots.low friction pivots. Follow the magnetic field lines of Follow the magnetic field lines of

the earth.the earth. Point towards the geographic north Point towards the geographic north

pole.pole.

Earth MagnetosphereEarth Magnetosphere Region that contains a mix of Region that contains a mix of

electrically charged particles.electrically charged particles. Electric and magnetic phenomena Electric and magnetic phenomena

dominate rather than gravitational dominate rather than gravitational phenomena.phenomena.

Shield earth from the solar wind is Shield earth from the solar wind is called bow shock.called bow shock.

Van Allen Radiation BeltsVan Allen Radiation Belts Traps high energy particles that Traps high energy particles that

leaked to magnetosphere.leaked to magnetosphere. Regions of particularly high Regions of particularly high

concentration of charged particles.concentration of charged particles. Are responsible for the aurora Are responsible for the aurora

(Northern and Southern Lights).(Northern and Southern Lights).

Conductors Conductors with with

CurrentCurrent

Conductors with CurrentConductors with Current

Electric current generate Electric current generate magnetic field.magnetic field.

Hans Christian Oersted noticed Hans Christian Oersted noticed that the electric current can that the electric current can influence a compass needle.influence a compass needle.

Oersed and Andre-Marie Ampere Oersed and Andre-Marie Ampere shows that current carrying shows that current carrying wires exert force to one another.wires exert force to one another.

Straight ConductorStraight Conductor

The direction of the magnetic The direction of the magnetic field in a straight conductor can field in a straight conductor can be determined using the be determined using the right-right-hand-rulehand-rule..

β

I

Conductor

Single-Loop ConductorSingle-Loop Conductor

The conductor maybe in the The conductor maybe in the shape of circle, ellipse or shape of circle, ellipse or polygon.polygon.

The magnetic field line’s The magnetic field line’s direction must be according to direction must be according to the right-hand-rule with the right-hand-rule with respect to the current.respect to the current.

I

β

The magnetic field vector at the The magnetic field vector at the center of the loop adds-up as one center of the loop adds-up as one big magnetic field vector.big magnetic field vector.

SolinoidSolinoid

Conducting wire coiled in the Conducting wire coiled in the shape of helix.shape of helix.

Function like several adjacent Function like several adjacent single-loop conductor.single-loop conductor.

Similar to the wire coiled around Similar to the wire coiled around an iron core (usually a nail) in an an iron core (usually a nail) in an electromagnet.electromagnet.

C

The magnetic field vectors add-The magnetic field vectors add-up at the center.up at the center.

An ideal solenoid is a solenoid of An ideal solenoid is a solenoid of infinite length and uniform magnetic infinite length and uniform magnetic field inside the coil.field inside the coil.

A real solenoid is a solenoid of limit A real solenoid is a solenoid of limit length. Its magnetic field is uniform length. Its magnetic field is uniform near the center but not uniform near near the center but not uniform near the ends.the ends.

Moving Moving Charged Charged ParticlesParticles

Moving Charged ParticlesMoving Charged Particles All magnetic fields are generated by All magnetic fields are generated by

charging electric fields.charging electric fields.

Moving charged particles generates electric Moving charged particles generates electric field. Currents generate electric field field. Currents generate electric field because it is made-up of moving charge.because it is made-up of moving charge.

+

-

Positive charge : Use Right-Hand-Rule

Negative charge : Use Left-Hand-Rule

If a charge is moving relative to a point, the If a charge is moving relative to a point, the electric field at that point due to the charge is electric field at that point due to the charge is changing. This on-going change generates changing. This on-going change generates magnetic field.magnetic field.

Note: Note: Charging Electric field generates magnetic fields.Charging Electric field generates magnetic fields.

E1E2

E3

++ ++ ++

E1E2 E3

Calculating the Magnetic Calculating the Magnetic FieldField

Biot-Savart LawBiot-Savart Law Where:Where:

µµoo = 4µ x 10 = 4µ x 10-7-7 Tm/A = 1.26 x 10 Tm/A = 1.26 x 10-6-6 Tm/A Tm/A

30

4 r

Idlxrd

r

dβ

I

dl

Ampere’s LawAmpere’s Law

encIdl 0.

r

I

dl

Different Different Conductor Conductor ConfigurationsConfigurations Long straight Long straight

conductor:conductor:r

I

20

Iβr

Long cylindrical conductor of radius RLong cylindrical conductor of radius ROutside the conductor* Inside the conductor*Outside the conductor* Inside the conductor*

20

2 R

Ir

r

I

20

R

rOutside

Inside

Iβ

r

I

40

Circular loop of Radius Circular loop of Radius rr Center of a circular arc with central angle Ø (in Radian)Center of a circular arc with central angle Ø (in Radian)

I

r

Ø

Complete circular loopComplete circular loop

r

I

20

I

I r

)(2 22

20

rz

Ir

Distance Distance zz away directly above or below the away directly above or below the center of circular loop.center of circular loop.

z

r

I

Long solenoid (almost Ideal) with number Long solenoid (almost Ideal) with number of turns (of turns (N N ) per unit length.) per unit length. Inside the solenoid and near the centerInside the solenoid and near the center

Outside the solenoidOutside the solenoid

nI0

0

N

Sample Problem:Sample Problem: Straight conductorStraight conductor::

What is the magnitude of the magnetic What is the magnitude of the magnetic field 6.1 m field 6.1 m below a power line in which below a power line in which there is a steady current there is a steady current of 100 A?of 100 A?

Field along a solenoid:Field along a solenoid:

A solenoid of length 30.0 cm and radius 2.0 A solenoid of length 30.0 cm and radius 2.0 cm is cm is closely winded with 200 turns of wire. closely winded with 200 turns of wire. The current in The current in the winding is 5.0 A. Compute the winding is 5.0 A. Compute the magnetic field the magnetic field magnitude at a point near magnitude at a point near the center of the solenoid.the center of the solenoid.

Parallel CurrentParallel Current The force between two parallel The force between two parallel

current current IIaa and and IIbb is given by: is given by:

Where:Where: LL = Length of the conductors = Length of the conductors d d = distance between the conductors= distance between the conductors

d

LIIF ba

20

The force is attractive if the currents The force is attractive if the currents are toward the same direction and are toward the same direction and repulsive if toward opposite repulsive if toward opposite directions.directions.

L

Ia

Ib d

Sample Problem:Sample Problem: Parallel CurrentsParallel Currents

Two long parallel wires are Two long parallel wires are separated by distance of 8.0 cm. The separated by distance of 8.0 cm. The current running along these wires current running along these wires are equal in magnitude but opposite are equal in magnitude but opposite direction.direction.

a)a) What is the current along the wires if What is the current along the wires if the magnitude field halfway between the magnitude field halfway between them is 300.0 N?them is 300.0 N?

b)b) What is the force between the wires What is the force between the wires if the length of both of them is 4.0 if the length of both of them is 4.0 m? Is this force attractive or m? Is this force attractive or repulsive?repulsive?

Magnetic Magnetic MaterialsMaterials

Atoms are like tiny magnets. Atoms are like tiny magnets. The electrons form a The electrons form a microscopic loop.microscopic loop.

Atoms are like tiny magnets. The Atoms are like tiny magnets. The electrons form a microscopic loop.electrons form a microscopic loop.

Moving electrons generate magnetic Moving electrons generate magnetic field. Hence, atoms are like small field. Hence, atoms are like small magnets.magnets.

Most objects do not generate magnetic Most objects do not generate magnetic field despite being made-up of atoms field despite being made-up of atoms because the atoms are oriented because the atoms are oriented randomly: the atoms cancel each other’s randomly: the atoms cancel each other’s magnetic field.magnetic field.

+

-

I

Types of Magnetic Types of Magnetic MaterialsMaterials

ParamagneticParamagnetic

FerromagneticFerromagnetic

DiamagneticDiamagnetic

Assignment:Research “Types of magnetic materials”Computerized, Short Bond paper.To be submitted next meeting.

Field SymmetryField SymmetryMagnetic Flux definedMagnetic Flux defined The magnetic flux (The magnetic flux (ΦΦββ ) is the strength ) is the strength

of an electric field over an area in a of an electric field over an area in a field region.field region. Where:Where:

ββ = Magnetic field (Tesla, T) = Magnetic field (Tesla, T) A = cross-sectional area (mA = cross-sectional area (m22)) θθ = Angle = Angle

cosAA

The term Magnetic flux density is The term Magnetic flux density is synonymous to magnetic field, defined as synonymous to magnetic field, defined as the magnetic flux per unit of the magnetic flux per unit of perpendicular areaperpendicular area

The SI unit of magnetic flux is weber The SI unit of magnetic flux is weber (Wb). (Wb). 1 Wb = 1 T*m1 Wb = 1 T*m22

N S

0

90cos 0

A

A

A

0cosβ

β

β

β

A

A

A

β

β

cosA

Conducting loop in a magnetic Conducting loop in a magnetic fieldfield

InductionInduction The process of producing current and emf The process of producing current and emf

by changing magnetic field.by changing magnetic field.

Induced currentInduced current The current produced by changing The current produced by changing

magnetic field.magnetic field.

Induced Induced emfemf The work done per unit change in The work done per unit change in

producing induced current.producing induced current.

Note:Note: Changing magnetic field generates electric Changing magnetic field generates electric

field.field.

N

S

Law Law of of

InductionInduction

Faraday’s LawFaraday’s Law States that the induced States that the induced emf emf in a in a

close loop equals the negative of the close loop equals the negative of the time rate of change of the magnetic time rate of change of the magnetic flux through the loop.flux through the loop.

t

Induced Induced emfemf appears on the appears on the conducting loop if any of the conducting loop if any of the following happens:following happens: The magnetic field is changing.The magnetic field is changing. The area of the loop within the The area of the loop within the

magnetic field is changing.magnetic field is changing. The conducting loop is rotating The conducting loop is rotating

while immersed to magnetic field.while immersed to magnetic field.


A single loop of wire with an A single loop of wire with an enclosed area of 6.00 cmenclosed area of 6.00 cm22 is in a is in a region of uniform magnetic field, region of uniform magnetic field, with the field perpendicular to the with the field perpendicular to the plane of the loop. The magnetic field plane of the loop. The magnetic field is decreasing at a constant rate of is decreasing at a constant rate of 0.150 T/s.0.150 T/s.

a)a) What is the induced What is the induced emf emf ??

b)b) If the loop has a resistance of 0.300 If the loop has a resistance of 0.300 ohms what is the current induced in the ohms what is the current induced in the loop?loop?

Lenz’s LawLenz’s Law

States that the induced current States that the induced current runs to the direction in such a runs to the direction in such a way that it generates magnetic way that it generates magnetic field to oppose the changes in field to oppose the changes in the magnetic flux that induced the magnetic flux that induced the current.the current.

Used in determining the direction of Used in determining the direction of induced current and induced induced current and induced emfemf..

S

N

β

S

N

β

S

N

β

βind

βind

I = 0 I I

(A) (B) (C)

No motion β increasing in the loop β decreasing in the loop

Problem Solving:Problem Solving:

A rectangular inductor of unknown A rectangular inductor of unknown length and width of 0.2 m moves at length and width of 0.2 m moves at 12 m/s to the right. It is oriented 12 m/s to the right. It is oriented perpendicular to a magnetic field of perpendicular to a magnetic field of 0.4 T.0.4 T.

a)a) What is the induced What is the induced emfemf in the circuit? in the circuit?

b)b) What is the direction of the induced emf?What is the direction of the induced emf?

c)c) If the resistance across the loop is 0.3 If the resistance across the loop is 0.3 ohms, What is the current?ohms, What is the current?

InductanceInductance

Tendency of an electrical circuit Tendency of an electrical circuit to oppose the starting, stopping to oppose the starting, stopping or changing the current.or changing the current.

Its SI unit is henry (H):Its SI unit is henry (H): 1H = 1 Tm1H = 1 Tm22/A/A

InductorInductor Provides inductance in a circuit.Provides inductance in a circuit. Produce uniform magnetic field.Produce uniform magnetic field. The inductance The inductance LL of an inductor of an inductor

with number of turns with number of turns NN is given by: is given by:

I

NL


A current of 5.0 mA passess A current of 5.0 mA passess through the solenoid inductor through the solenoid inductor with 400 turns and inductance with 400 turns and inductance of 8.0 mH. What is the of 8.0 mH. What is the magnetic flux through the magnetic flux through the coil?coil?

Self-inductanceSelf-inductance happens when happens when two adjacent turns of a solenoid two adjacent turns of a solenoid inductor induced one another to inductor induced one another to changing electric current.changing electric current.

The result of this is the intended The result of this is the intended function of the inductor: function of the inductor: to resist changes in current.to resist changes in current.

Self-inductanceSelf-inductance

I I

CURRENTDECREASING

CURRENTINCREASING

εεLL

εεLL

εεLL

εεLL The The self-induced emfself-induced emf is the is the emfemf that that

arises due to the turns in the inductor arises due to the turns in the inductor inducing one another: Self induced inducing one another: Self induced emfemf opposes the current.opposes the current.

The self-induced The self-induced emfemf can be can be solved using the formula:solved using the formula:

t

ILL

The inductance does not oppose the The inductance does not oppose the current itself, only the change in current. It current itself, only the change in current. It opposes both increase and decrease in opposes both increase and decrease in current.current.

InductanceL

Inductor

If the current is increasing

then the voltageOpposing thatChange is createdBy the magneticField of the coil.

Mutual-Inductance (M)Mutual-Inductance (M)

Proportionality between the Proportionality between the emfemf generated in a coil to the change in generated in a coil to the change in current in the other coil which produces it.current in the other coil which produces it.

Arises when to coils in close proximity Arises when to coils in close proximity induces induces emfemf to one another. to one another.

2

1

1

2

1221

1221

I

N

I

NM

MMM

Notation: the subscript that the stand for the Notation: the subscript that the stand for the inducing coil comes second and the subscript that inducing coil comes second and the subscript that stands for the coil being induced comes first.stands for the coil being induced comes first.

Equation of induced emf:Equation of induced emf:εε2121 is the emf induced in coil is the emf induced in coil 2 due to change in current in coil 1 and 2 due to change in current in coil 1 and εε1212 is the emf is the emf induced in coil 1 cue to change in current in coil 2. induced in coil 1 cue to change in current in coil 2.

t

IM

t

IM

21212

12121


Two single-turn coils are fixed in Two single-turn coils are fixed in location such that they can induced location such that they can induced emf to one another.emf to one another.

a)a) When the first coil has no current and When the first coil has no current and the current in the second coil increases the current in the second coil increases at rate of 15.0 A/s, the emf in the first at rate of 15.0 A/s, the emf in the first coil is 25.0 mV. What is their mutual coil is 25.0 mV. What is their mutual inductance?inductance?

b)b) When the second coil has no current and When the second coil has no current and the first coil has current of 3.60 A, What the first coil has current of 3.60 A, What is the flux linkage in the second coil?is the flux linkage in the second coil?

Alternating CurrentAlternating Current Alternating current (ac)Alternating current (ac)

The current is not constant, but varies The current is not constant, but varies sinusoidally with time.sinusoidally with time.

I

t

Advantages over direct current Advantages over direct current (dc)(dc)

Easier than transmit since charge Easier than transmit since charge carriers are not required to travel carriers are not required to travel over long distance.over long distance.

Enables transformers to work by Enables transformers to work by utilizing Faraday’s Law of induction.utilizing Faraday’s Law of induction.

More readily adaptable to rotating More readily adaptable to rotating machineries such as generators and machineries such as generators and electric motors.electric motors.

Alternating Current GeneratorAlternating Current Generator

The emf The emf εε varies sinusoidally with time: varies sinusoidally with time:

Driving frequency Driving frequency ffd d ::

)sin( tdm

dd f 2

Where:Wd = Angle of frequency of the emft = timeεm = amplitude of the emf

The current The current II varies sinusoidally with time: varies sinusoidally with time:

)sin( tII dm

Oscillating Oscillating CircuitCircuit

Resistive LoadResistive Load The phase constant is zero.The phase constant is zero.

Time-varying voltage:Time-varying voltage:

Where:Where:

VVRR = voltage across the resistor = voltage across the resistorVVRmRm = amplitude of the voltage = amplitude of the voltage

Time-varying current:Time-varying current:

Where:Where: I I R R = current through the resistor= current through the resistor

I I Rm Rm = amplitude of the current= amplitude of the current

Relation of amplitude of current and voltage:Relation of amplitude of current and voltage:

)sin( tVV dRmR RI I

ε)sin( tII dRmR

RIV RmRm

0

Capacitive LoadCapacitive Load The phase constant isThe phase constant is

Time-varying voltageTime-varying voltage

Where:Where:VVcc = voltage across the Capacitor = voltage across the Capacitor

VVccmm = amplitude of the voltage = amplitude of the voltage


Where:Where:

I cI c = current through the Capacitor= current through the Capacitor

II c cm m = amplitude of the current= amplitude of the current

)sin( tVV dCmC

CI

I

ε

2900

)90sin( 0 tII dCmC


The Quantity XThe Quantity XCC is called capacitive is called capacitive reactance:reactance:

The unit of reactance is ohms (The unit of reactance is ohms (ΩΩ))

CX

dC

1

CCmCm XIV

Inductive LoadInductive Load The phase constant is:The phase constant is:

Time-varying voltageTime-varying voltage

Where:Where:VVLL = voltage across the inductor = voltage across the inductorVVLLmm = amplitude of the voltage = amplitude of the voltage


Where:Where:I I L L = current through the inductor= current through the inductor

I I LLmm = amplitude of the current = amplitude of the current

)sin( tVV dLmL

)90sin( 0 tII dLmL

2900

I I

ε

L


The Quantity XThe Quantity XLL is called inductance is called inductance reactance:reactance:

The unit of reactance is ohms (The unit of reactance is ohms (ΩΩ))

LLmLm XIV

LX dL

RLC Series CircuitRLC Series Circuit The Resistor, Inductor and Capacitor are The Resistor, Inductor and Capacitor are

connected in series with ac connected in series with ac emf emf device.device.

ε

LR

C

II

II

Voltage and current in series circuit:Voltage and current in series circuit:

Relation of the amplitudes of voltage and Relation of the amplitudes of voltage and current:current:

LCR

LCR

VVV

IIII

ZIm

The quantity is called Impedance (Z):The quantity is called Impedance (Z):

The unit of reactance is ohms (The unit of reactance is ohms (ΩΩ).). The phase constant can be solved using The phase constant can be solved using

the equation:the equation:

22 )( CL XXRZ

R

XX CL tan


A 160A 160ΩΩ resistor, 15.0 resistor, 15.0µF capacitor and 230 µF capacitor and 230 mH inductor are connectedmH inductor are connected to form RLC to form RLC circuit with an ac generator whose circuit with an ac generator whose conducting loop rotates at 60.0 full rotation conducting loop rotates at 60.0 full rotation per second and with per second and with emfemf amplitude of 36.0 amplitude of 36.0 V.V.

Find:Find:a)a) The impedance of the circuit.The impedance of the circuit.

b)b) The current flowing through the circuit.The current flowing through the circuit.

c)c) The phase constantThe phase constant

TransformerTransformer A device used to change the A device used to change the

voltage and current levels in an voltage and current levels in an AC circuit.AC circuit.

Step-up transformer: VStep-up transformer: Voutout > V > Vinin

Step-down transformer: VStep-down transformer: Vinin > V > Voutout

inputoutput

Primary winding Secondary windingcore

Magnetic flux

Transformer

Characteristic of an Ideal Characteristic of an Ideal TransformerTransformer

Has two coil or windings, electrically Has two coil or windings, electrically insulated from each other but wound insulated from each other but wound on the same core.on the same core. Core typically made-up of material with Core typically made-up of material with

large relative permeability such as iron.large relative permeability such as iron. Primary coil (input) – winding to which Primary coil (input) – winding to which

power supply is received.power supply is received. Secondary coil (output) – winding to which Secondary coil (output) – winding to which

power is delivered.power is delivered. Resistance is negligible.Resistance is negligible. Magnetic field is confined to the iron Magnetic field is confined to the iron

core.core.

Transformation of voltage and Transformation of voltage and currentcurrent

The induced The induced emfemf in primary, in primary, εε11, and , and secondary coil, secondary coil, εε22 are: are:

We can combine the equation above as:We can combine the equation above as:

tN

tN

22

11

2

1

2

1

N

N

Terminal voltage of primary and secondary Terminal voltage of primary and secondary coil:coil:

Step-up transformer, Step-up transformer, εε22 > > εε11 and and NN22 > > NN11

Step-down transformer, Step-down transformer, εε11 > > εε22 and and NN11 > > NN22

2

1

2

1

N

N

V

V

Power of Transformer:Power of Transformer:

If we place a resistance, R, to complete If we place a resistance, R, to complete the circuit in the secondary coil:the circuit in the secondary coil:

2211 VIVIP

2

1

21

1

NN

R

I

V


A transformer has 100 turns on A transformer has 100 turns on its primary coil and 300 turns on its primary coil and 300 turns on the secondary coil. If the primary the secondary coil. If the primary voltage is 110.0 V and primary voltage is 110.0 V and primary current is 5.00 A. What are the current is 5.00 A. What are the secondary voltage and current?secondary voltage and current?

Nature of Nature of WavesWaves

WavesWaves

A disturbance that travels through a A disturbance that travels through a material medium.material medium.

Carries energy.Carries energy. Can transfer energy from one place to Can transfer energy from one place to

another without actual motion of an another without actual motion of an object or particle.object or particle.

Some waves can travel through Some waves can travel through vacuum and do not require a material vacuum and do not require a material medium;medium;

Example is Example is LightLight

Types of WavesTypes of Waves

Transverse waveTransverse wave The motion of the particles at The motion of the particles at

the moment the disturbance the moment the disturbance passes through is passes through is perpendicular to the perpendicular to the propagation of the wave.propagation of the wave.Example: LightExample: Light

Wave propagation

Wave propagation

Wave propagation

Particle motion

Particle motion

Particle motion

Undisturbed position



Longitudinal WaveLongitudinal Wave The motion of the particles at The motion of the particles at

the moment the disturbance the moment the disturbance passes through is linear to the passes through is linear to the propagation of the wave.propagation of the wave.Example: SoundExample: Sound

Wave propagation

Wave propagation

Wave propagation

Particle motion

Particle motion

Particle motion




Properties of WaveProperties of Wave

WavelengthWavelength

The distance between two The distance between two adjacent particles or points that adjacent particles or points that behave in the same manner.behave in the same manner.

The unit is meter (m).The unit is meter (m). Denoted by Greek letter Denoted by Greek letter

(“lamda” (“lamda” λλ))

PeriodPeriod

The time it takes for The time it takes for one complete one complete wavelength to pass wavelength to pass through a certain through a certain point.point.

The unit is second The unit is second (s).(s).

Denoted as capital T.Denoted as capital T.

fT

1

FrequencyFrequency

The number of wave The number of wave passing through a certain passing through a certain point per unit time.point per unit time.

The unit is per second or The unit is per second or hertz (/s or shertz (/s or s-1-1))

Reciprocal of Period (T)Reciprocal of Period (T) Denoted by small letter Denoted by small letter ff..

Tf

1

AmplitudeAmplitude

The maximum displacement of The maximum displacement of particle due to disturbance particle due to disturbance before returning to its before returning to its undisturbed position.undisturbed position.

The unit is meter (m).The unit is meter (m). Denoted by capital letter A.Denoted by capital letter A.

SpeedSpeed

Distance traveled by Distance traveled by the disturbance per the disturbance per unit of time.unit of time.

The Unit is meter per The Unit is meter per second (m/s).second (m/s).

Denoted by small Denoted by small letter v.letter v.

tv

λ

λ

A

A

crest

trough

fT

1

tv

QuantityQuantity SymbolSymbol unitunit relationrelationWavelengthWavelength λλ Meter (m)Meter (m)

PeriodPeriod TT Second (s)Second (s)

frequencyfrequency ff /s, s/s, s-1-1

Hertz (Hz)Hertz (Hz)

amplitudeamplitude AA Meter (m)Meter (m)

speedspeed vv m/sm/s

Tf

1

fv


The frequency of a wave The frequency of a wave traveling across the string is traveling across the string is 0.167 Hz and its wavelength is 0.167 Hz and its wavelength is 9.00 cm. What is the period and 9.00 cm. What is the period and speed of the wave?speed of the wave?

Behavior of WaveBehavior of Wave

RefractionRefraction It is the change in the wave’s direction as it It is the change in the wave’s direction as it

crosses the boundaries between two mediumcrosses the boundaries between two medium

Incident

Refracted

Medium 1 Medium 2

ReflectionReflection It is the change in the wave’s direction It is the change in the wave’s direction

without crossing to the adjacent medium.without crossing to the adjacent medium.

Incident

Reflected

Medium 1 Medium 2

InterferenceInterference It is the combination of two or It is the combination of two or

more waves as they pass more waves as they pass through the same location at through the same location at the same time.the same time.

Two kinds of InterferenceTwo kinds of Interference Constructive interferenceConstructive interference

It happens when the waves passing It happens when the waves passing through the same location are in-through the same location are in-phase, resulting to a combined phase, resulting to a combined disturbance with higher amplitude.disturbance with higher amplitude.

Destructive interferenceDestructive interference It happens when the waves passing It happens when the waves passing

through the same location are out-through the same location are out-phase, resulting to a cancelled phase, resulting to a cancelled disturbance with lower or zero disturbance with lower or zero amplitude.amplitude.

DiffractionDiffraction It is the spreading of wave after it passed It is the spreading of wave after it passed

through a small slit.through a small slit. Each point at the Each point at the wavefront wavefront acts as tiny acts as tiny

source of smaller waves called source of smaller waves called wavelets. wavelets. The The interference among wavelets keep wave in interference among wavelets keep wave in shape.shape.

However, However, If the slit is small enough, some of If the slit is small enough, some of the wavelets will not be able to pass through; the wavelets will not be able to pass through; with no interference, the wavelets from one with no interference, the wavelets from one point will be able to propagate.point will be able to propagate.

wavefrontsslit

obstacleDiffracted wave

ElectromagnetiElectromagnetic Wavec Wave

Changing electric field creates Changing electric field creates magnetic field.magnetic field.

Changing magnetic filed creates Changing magnetic filed creates electric filed.electric filed.

Electromagnetic wavesElectromagnetic waves are are disturbance produced by propagating disturbance produced by propagating electric and magnetic fields.electric and magnetic fields.

Speed in a vacuumSpeed in a vacuum: : (299,792,458 m/s or 3.00 x 10(299,792,458 m/s or 3.00 x 1088 m/s) m/s) Examples:Examples:

LightLight Infrared raysInfrared rays Ultraviolet raysUltraviolet rays Radio wavesRadio waves raysrays

LightLight is the electromagnetic wave is the electromagnetic wave that is visible to the eyes, with that is visible to the eyes, with wavelengths between 4 x10wavelengths between 4 x10-7-7 m and 7 m and 7 x10x10-7-7 m and frequencies between 7 x m and frequencies between 7 x 10101414 hertz and 4 x10 hertz and 4 x101414 hertz. hertz.

Electric field

Magnetic field Direction

Wavelength

Speed in a vacuumSpeed in a vacuum

smxE

c /1000.31 8

00

Where:c= speed of the electromagnetic waves

(m/s)E=electric field (V/m)β=magnetic field (Weber/m2)εo=permitivity constantμo=permeability constant


At a particular time the At a particular time the magnetic field intensity in magnetic field intensity in electromagnetic wave is 2 x10electromagnetic wave is 2 x10--

1010 Wb/m Wb/m22. Calculate the . Calculate the magnitude of the electric field magnitude of the electric field intensity.intensity.

Electromagnetic Electromagnetic SpectrumSpectrum

Assignment:Assignment: Computerized, Short bond paperComputerized, Short bond paper

Research workResearch work Gamma RaysGamma Rays X-raysX-rays Ultraviolet raysUltraviolet rays Visible LightVisible Light InfraredInfrared Radio waveRadio wave

Wavelength and Wavelength and frequencyfrequency

The frequency and wavelength of The frequency and wavelength of electromagnetic (EM) wave are electromagnetic (EM) wave are inversely proportional.inversely proportional.

c

f

Where:f = frequency of the wave (Hz)c = speed of the EM wave in a vacuumλ=wavelength (m)


What is the range of the What is the range of the wavelength of the visible light?wavelength of the visible light?(see… Electromagnetic spectrum (see… Electromagnetic spectrum

table)table)

Visible LightVisible Light

Visible LightVisible Light Form of electromagnetic radiation that Form of electromagnetic radiation that

our eyes detect.our eyes detect. Wavelength ranging from 400 to 760 Wavelength ranging from 400 to 760

nm.nm. People are able to “see” an object People are able to “see” an object

ligth enters the eyes.ligth enters the eyes. Represented as:Represented as:

RayRay a thin beam of light that travel in a straight line.a thin beam of light that travel in a straight line.

WavefrontWavefront It is the line (not necessarily straight) or surface It is the line (not necessarily straight) or surface

connecting all the light that left a source at the connecting all the light that left a source at the same time.same time.

Can be reflected and refracted.Can be reflected and refracted.

OpticsOptics

Branch of electromagnetism that Branch of electromagnetism that deals with the nature, properties and deals with the nature, properties and behavior of light.behavior of light.

Two branches:Two branches: Geometric OpticsGeometric Optics

Describes light propagation in terms of rays.Describes light propagation in terms of rays. Physical OpticsPhysical Optics

Treat light propagation as a wave Treat light propagation as a wave phenomenon rather than a ray phenomenon.phenomenon rather than a ray phenomenon.

Reflection of LightReflection of Light

The angle of incident (The angle of incident (θθii) is equal to ) is equal to the angle of reflection (the angle of reflection (θθrr) )

ri

θi θr

θi= 0θr = 0

Mirror AThe light is parallel toThe plane of mirror.

No Reflection.

Mirror BLight is reflected

at an angle.θi= θr

A B

Mirror CIncident and

reflectedLight are both perpendicularTo the plane of

mirror.θi-θr=0

C

Refraction of LightRefraction of Light

The refraction of light is The refraction of light is governed by Snell’s Law:governed by Snell’s Law:

rrii nn sinsin

Where:θi= angle of incident rayθr= angle of refraction rayni & nr = indices of

refraction

AIR

WATER

Incident ray

Refracted ray

θi

θr

rwateriair nn sinsin

Index of refraction (n)Index of refraction (n) The ratio of light’s speed in a vacuum The ratio of light’s speed in a vacuum

and light’s speed in that material.and light’s speed in that material. Property of the material has no unit.Property of the material has no unit.

v

cn

Where:c = 3.00 x108

m/s light in

vacuum.v = speed of

light in the

medium.

Sample Problem:

A light beam crosses from the A light beam crosses from the vacuum to water with incident vacuum to water with incident beam angle of 25.0beam angle of 25.000. If the index . If the index of refraction of vacuum is 1 and of refraction of vacuum is 1 and that of water is 1.33, what is the that of water is 1.33, what is the angle of refracted light beam?angle of refracted light beam?

MirrorsMirrors

Surface that reflects so much light that Surface that reflects so much light that they formed images.they formed images.

Made of polish metal (silver or copper) Made of polish metal (silver or copper) or glass with silver colored coating.or glass with silver colored coating.

Two kinds of mirror:Two kinds of mirror: Plane mirrorPlane mirror

Flat surface and the reflected Flat surface and the reflected parallel light rays remain parallel.parallel light rays remain parallel.

Plane mirror

Spherical mirrorSpherical mirror Its surface form a part of the Its surface form a part of the surface of the sphere:surface of the sphere:

Concave mirror – focuses reflected rays.Concave mirror – focuses reflected rays. Convex mirror – scatters reflected rays.Convex mirror – scatters reflected rays.

Concave mirror Convex mirror

PrincipalAxis

PrincipalAxis

Parts of a mirrorParts of a mirror

Principal axisPrincipal axis An imaginary line passing through An imaginary line passing through

the center of the sphere and passing the center of the sphere and passing through the exact center of the through the exact center of the mirror.mirror.

Center of Curvature (C)Center of Curvature (C) The point in the center of the sphere The point in the center of the sphere

from which the mirror was sliced.from which the mirror was sliced.

Vertex (V)Vertex (V) The point on the mirror’s surface where The point on the mirror’s surface where

the principal axis meets the mirror.the principal axis meets the mirror. The geometric center of the mirror.The geometric center of the mirror.

Focal point (F)Focal point (F) A point between the vertex and the A point between the vertex and the

center of the curvature.center of the curvature. In concave mirrors, this is the point In concave mirrors, this is the point

where the reflected rays intersect.where the reflected rays intersect. In convex mirror, this is the point from In convex mirror, this is the point from

where the reflected ray apparently where the reflected ray apparently originates.originates.

Radius of the curvature (R)Radius of the curvature (R) Distance from the vertex to the center of Distance from the vertex to the center of

the curvature.the curvature. The radius of the sphere from which the The radius of the sphere from which the

mirror was cut.mirror was cut. Focal Length (f)Focal Length (f)

The distance from the mirror to the focal The distance from the mirror to the focal point.point.

One-half the radius of the curvature.One-half the radius of the curvature. For concave mirrors:For concave mirrors:

For convex mirrors:For convex mirrors:

2

Rf

2

Rf


Light from the distance is Light from the distance is collected by a concave mirror. collected by a concave mirror. How far from the mirror do the How far from the mirror do the light rays converge if the light rays converge if the radius of curvature of the radius of curvature of the mirror is 200 cm.?mirror is 200 cm.?

Mirrors Image FormationMirrors Image Formation

In Plane mirrorIn Plane mirror In order to see the image of an In order to see the image of an

object in a mirror:object in a mirror: You must view at the image;You must view at the image; When you view at the image, light will When you view at the image, light will

come to your eyes along that line of come to your eyes along that line of sight.sight.

The image location is located at that The image location is located at that position where observers are position where observers are viewing the image of an object. It is viewing the image of an object. It is the location behind the mirror where the location behind the mirror where all the light appears to diverge from.all the light appears to diverge from.

An image is formed because light An image is formed because light emanates from the object in a emanates from the object in a variety of directions.variety of directions.

Some of this light reaches the Some of this light reaches the mirror and reflects off the mirror mirror and reflects off the mirror accordingly to the law of reflection.accordingly to the law of reflection.

In Concave mirrorIn Concave mirror There are two types of image:There are two types of image:

Real imageReal image Light passes through the Light passes through the image’s location.image’s location.

Its formed when p > fIts formed when p > f Virtual imageVirtual image

Light does not pass through the Light does not pass through the image’s location.image’s location.

Its formed when p < f Its formed when p < f

In Convex mirrorIn Convex mirror

The image is always virtual.The image is always virtual.

V

Mirror

C F

For Concave Mirror

Principal axis

R

f

Object

V

Mirror

CF

For Convex Mirror

Principal axis

f

Object

Mirror EquationMirror Equation

Where:Where:f = focal lengthf = focal lengthp = Object distancep = Object distance

Distance from the Distance from the object to the mirror.object to the mirror.

q = Image distanceq = Image distance Distance from the Distance from the

image to the mirror. image to the mirror. m = Magnification of the m = Magnification of the mirrormirrory = size of the objecty = size of the objecty’ = size of the imagey’ = size of the image

qpf

111

p

q

y

ym

'

V

Mirror

C

For Concave Mirror

Principal axis

p

f

Object

qF

Image

Ray Diagram Method Ray Diagram Method (RDM)(RDM)

For Concave mirror:For Concave mirror: First Ray – Parallel to the axis, First Ray – Parallel to the axis,

reflects to the mirror, then passing reflects to the mirror, then passing through focal point.through focal point.

Second Ray – Passing through the Second Ray – Passing through the focal point, reflect to the mirror, focal point, reflect to the mirror, then parallel to the axis.then parallel to the axis.

Third Ray – Passing through center Third Ray – Passing through center of curvature, then bounce back. of curvature, then bounce back.

V

Mirror

C

Principal axis

Y

F

Image

RDMRDM

1st Ray

2nd Ray3 rd Ray

Object

Concave Mirror


A 3.0 cm tall light bulb is A 3.0 cm tall light bulb is placed a distance of 40 cm placed a distance of 40 cm from a concave mirror having a from a concave mirror having a focal length of 10.2 cm. focal length of 10.2 cm. Determine the image distance.Determine the image distance.

LENSESLENSES It is an optical system with It is an optical system with

two refracting surfaces.two refracting surfaces.

Thin LensThin Lens

Has two spherical surfaces close Has two spherical surfaces close enough so its thickness can be enough so its thickness can be neglected.neglected.

Types of Thin lensTypes of Thin lensConverging LensConverging LensDiverging LensDiverging Lens

Converging LensConverging Lens Different kinds of converging lens:Different kinds of converging lens:

Meniscus Piano-convex Double-convex

Diverging LensDiverging Lens Different kinds of diverging lens:Different kinds of diverging lens:

Meniscus Piano-concave Double-concave

Parts of LensesParts of Lenses Optic axisOptic axis

The central horizontal line defined The central horizontal line defined by the centers of curvature of the by the centers of curvature of the two spherical surfaces.two spherical surfaces.

Focal points (FFocal points (F11 and F and F22)) Focal Length (f)Focal Length (f)

Distance between a focal point and Distance between a focal point and the center of the lensthe center of the lens

The two focal lengths are always The two focal lengths are always equal for a thin lensequal for a thin lens

Image Formation by thin lensesImage Formation by thin lenses

Real image are located on the side of Real image are located on the side of the lens opposite that of the object.the lens opposite that of the object.

Virtual images are located on the Virtual images are located on the same side of the lens as the objectsame side of the lens as the object

F1 F2

f f

Optic axis

Converging lensConverging lens

When a beam of parallel rays pass through the When a beam of parallel rays pass through the lens, the rays converge at one focal point.lens, the rays converge at one focal point.

Its focal length is defined to be positive.Its focal length is defined to be positive.

F2F1

f f F2F1

f f

Optic axis

Optic axis

Converging lens can form either Converging lens can form either real or virtual image.real or virtual image.

Real image if the distance of the Real image if the distance of the object from the center of the lens is object from the center of the lens is greater than the focal length (p>f).greater than the focal length (p>f).

Virtual image if the distance of the Virtual image if the distance of the object from the center of the lens is object from the center of the lens is less than the focal length (p<f).less than the focal length (p<f).

Image formation by Thin Image formation by Thin LensesLenses

Real ImageReal Image

F1

F2

Object

Image

f f

p q

Optic axis

Virtual ImageVirtual Image

F1

ObjectF2

f f

Image

p

q

Optic axis

F1F2

f f

Optic axis

Diverging lensDiverging lens

When a beam of parallel rays are incident on When a beam of parallel rays are incident on this lens, the rays diverge after refraction.this lens, the rays diverge after refraction.

Its focal length is defined to be negative.Its focal length is defined to be negative.

F2

F1

f f

F2 F1

f f

Optic axis

Optic axis

Image formation by Thin Image formation by Thin LensesLenses

F1

F2

Object

Image

f f

p

q

The image formed by a diverging lens is always virtual.

Optic axis

Lens EquationLens Equation

qpf

111

p

qm

Thin Lens equation:

Lateral magnification:


A converging lens has a A converging lens has a focal length of 12.0 cm for focal length of 12.0 cm for an object 20.0 cm to the left an object 20.0 cm to the left of the lens,of the lens,

Determined:Determined:

a)a) The image positionThe image position

b)b) The image magnificationThe image magnification

Lenses and MirrorLenses and Mirror

Assignment:Assignment: Computerized, Short bond paperComputerized, Short bond paper

Research workResearch work The EyeThe Eye The CameraThe Camera The Magnifying GlassThe Magnifying Glass The Telescope (Galileo)The Telescope (Galileo) The MicroscopeThe Microscope

physics

Education

net charge

unit of charge

negative charge

identical charge

new charge

kind of electric charge

charge coulomb n

net positive charge