1103 103 physics for bioscience (part ii) electricity magnetism waves sound optics by dr. chittakorn...

1103 103 Physics 1103 103 Physics for Bioscience (Part II)for Bioscience (Part II)

• Electricity• Magnetism • Waves • Sound • Optics

by Dr. Chittakorn polyon

Department of Physics, Faculty of Science,Ubon Ratchathani University

AssessmentAssessment

• Quiz 5%• Homework 10%• Final 35%

ElectrostaticsElectrostaticsElectric FieldsElectric Fields

Text BooksText Books• Physics for Scientists and Engineers

6th Eds– Raymond A. Serway

Properties of Electric Properties of Electric ChargesCharges

• There are two kinds of charges in nature– Positive charge– Negative charge Benjamin Franklin (1706–1790)

• C harges of the same sign repel one another

• C harges with opposite signs attract on e another


• Total charge in an isol ated system is conser

ved.• Charge is quantized.

– q=NeRobert Millikan (1868–1953)

Charging Objects By Induction

• materials in terms of the ability of electrons to move through the material– Electrical conductors

• materials in which some of the electrons are free electrons that are not bound to atoms and can move relatively freely through the material

– copper, aluminum, silver

– Electrical insulators• materials in which all electrons are bound to atoms and

cannot move freely through the material– Glass, rubber, wood

MaterialsMaterials• materials in terms of the ability of

electrons to move through the material– Semiconductors

• Materials in which their electrical properties are somewhere between those of insulators and those of conductors

– Silicon, germanium

Charging Objects By Charging Objects By InductionInduction

Coulomb’s LawCoulomb’s Law• Properties of the electric force between

two stationary charged particles Charles Coulomb (1736–1806)

– inversely proportional to the square of the separation r between the particles and directed along the line joining them

– proportional to the product of the charges q1 and q2 on the two particles

– attractive if the charges are of opposite sign and repulsive if the charges have the same sign

– a conservative force

Coulomb’s LawCoulomb’s Law

221

r

qqkF ee

ke = 1/(4o) Coulomb constant

= 8.9875 × 109 N.m2/C2

o = 8.8542 × 1012 C2/N.m2

Permittivity of free space


1 212 2

ˆe

q qF k r

r

Example #1Example #1• Consider three point

charges located at the corners of a right triangle as shown in the figure, where q1=q3=5.0 C, q2=-2.0 C, and a=0.10 m. Find the resultant force exerted on q3

The Electric FieldThe Electric Field

The Electric FieldThe Electric Field• The electric force acting on a positive test

charge placed at that point divided by the test charge

0

eFEq

N/C


02ˆe e

qqF k r

r

2

0

ˆee

F qE k r

q r


• at any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges

2ˆie i

i i

qE k r

r

Example #2Example #2

• A charge q1=7.0 C is located at the origin, and a second charge q2=-5.0 C is located on the x axis, 0.30 m from the origin as shown in the figure. Find the electric field at the point P, which has coordinates

Electric Field of a ContinuousElectric Field of a ContinuousCharge DistributionCharge Distribution

2ˆie

i i

qE k r

r

2ˆe

qE k r

r

2 20ˆlim

i

ie i eq

i

q dqE k r k

r r

Discrete

Continuous

Electric Field of a ContinuousElectric Field of a ContinuousCharge DistributionCharge Distribution

• Charge density– The uniformly distribution of charges on a line,

a surface, or throughout a volume• linear charge density ()

– a charge Q is uniformly distributed along a line of length l (=Q/l)

• surface charge density ()– a charge Q is uniformly distributed on a surface of area

A (=Q/A)

• volume charge density ()– a charge Q is uniformly distributed throughout a

volume V (=Q/V)

Electric Field LinesElectric Field Lines

• Lines that are parallel to the electric field vector at any point in space

Electric Field LinesElectric Field Lines• The number of lines per unit area

through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region

• The field lines are close together where the electric field is strong and far apart where the field is weak

Rules for Drawing Electric Rules for Drawing Electric Field LinesField Lines

• The lines must begin on a positive charge and terminate on a negative charge.

• In the case of an excess of one type of charge, some lines will begin or end infinitely far away.

• The number of lines drawn leaving a positive charge or approaching a negative

charge is proportional to the magnitude of the charge.

• No two field lines can cross.

Motion of Charged Particles Motion of Charged Particles in a Uniform Electric Fieldin a Uniform Electric Field

• When a particle of charge q and mass m is placed in an electric field E, the electric force exerted on the charge causes the particle to accelerate with magnitude of a, where

F qE ma


• A positive point charge q of mass m is released from rest in a uniform electric field E directed along the x axis, as shown in the figure, Describe its motion

Gauss’s LawGauss’s Law• Electric Flux (E)

– The number of electric field lines penetrating some surface

E EA N.m2/C

Electric FluxElectric Flux

cosE EA EA


0limi

E i iAi Surface

E A E dA


E E dA


• Consider a uniform electric field E oriented in the x direction. Find the net electric flux through the surface of a cube of edge length l, oriented as shown in the figure.

Gauss’s LawGauss’s Law• a general relationship between the net

electric flux through a closed surface (often called a gaussian surface) and the charge enclosed by the surface

0E

qE dA E dA

Gauss’s LawGauss’s Law• The net flux through any

closed surface surrounding a point charge q is given by q/0 and is independent of the shape of that surface

Gauss’s LawGauss’s Law• The net electric flux through

a closed surface that surrounds no charge is zero

• The electric field due to many charges is the vector sum of the electric fields produced by the individual charges

1 2 3( ...).E E dA E E E dA

Gauss’s LawGauss’s Law

0

inE

qE dA


• Starting with Gauss’s law, calculate the electric field due to an isolated point charge q

Quiz #6Quiz #6

• Find the electric fiel d due to an infinite

plane of positive ch arge with uniform s

urface charge densi ty

Electric PotentialElectric Potential• Electric Potential • Potential Difference • Potential Differences in a Uniform

Electric Field

Electric PotentialElectric Potential• The potential energy per unit charge U/q0

is independent of the value of q0 and has a value at every point in an electric field

0

UV

q V

Potential DifferencePotential Difference• The change in potential energy of the

system when a test charge is moved between the points divided by the test charge q0

0

B

B A

A

UV V V E ds

q

Potential Differences in Potential Differences in a Uniform Electric Fielda Uniform Electric Field

B B

B A

A A

V V V E ds E ds Ed

B AV V


?B AV V

?C AV V


• A battery produces a specified potential difference V between conductors attached to the battery terminals. A 12-V battery is connected between two parallel plates, as shown in the figure. The separation between the plates is d = 0.30 cm, and we assume the electric field between the plates to be uniform.

Electric Potential and Potential Electric Potential and Potential Energy due to Point ChargesEnergy due to Point Charges

2

1 1B

A

r rBe

B A e er r B AA

k qdrV V V k q k q

r r r r

Electric Potential due to Electric Potential due to Point ChargesPoint Charges

• The electric potential created by a point charge at any distance r from the charge is

ek qVr

At rA = VA =0

Potential Energy due to Potential Energy due to Point ChargesPoint Charges

• If two point charges are separated by a distance r12, the potential energy of the pair of charges is given by

1 2

12

ek q qUr

CapacitCapacitoror• A device that store electric charge

– a combination of two conductors carryin g charges of equal magnitude and opposi te sign

CapacitCapacitance (ance (CC))• T he ratio of the magnitude of the charge

(Q) on either conductor to the magnitude o f the potential difference (V) between the

conductors– always a positive quantity

QC

V

Farad, F

- Parallel Plate Capacitors- Parallel Plate Capacitors

0ACd

• T - he capacitance of a parallel plate cap acitor is proportional to the area of its plates and inversely proportional to th

e plate separation

0 0

QE

A

0

QdV Ed

A

EE lectric lectric FF ield ield PP attern of attern of a a PP -arallel-arallel PP late late CCapacitorapacitor

A A CC ircuit ircuit with a Cwith a Capacitorapacitor

Combinations of Capacitors Combinations of Capacitors

• The individual potential differences across capacitors connected in parallel are the same and are equal to the potential difference applied across the combination

• T he total charge on capacitors connected in paralle l is the sum of the charges on the individual capacitors

• T he equivalent capacitance of a parallel combinatio n of capacitors is the algebraic sum of the individua

l capacitances and is greater than any of the individ ual capacitances

Parallel Combination Parallel Combination

Combinations of Capacitors Combinations of Capacitors

• T he charges on capacitors connected in series are the same

• T he total potential difference across any number of capacitors connected in series is the sum of the

potential differences across the individual capacitors

• T he inverse of the equivalent capacitance is the al gebraic sum of the inverses of the individual capa citances and the equivalent capacitance of a serie

s combination is always less than any individual c apacitance in the combination

Series Combination Series Combination

Energy Stored in Energy Stored in a Charged Capacitor a Charged Capacitor

221 1

( )2 2 2

QU Q V C V

C

1103 103 physics for bioscience (part ii) electricity magnetism waves sound optics by dr. chittakorn...

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