Electricity and Magnetism

Unit III

I Electrostatics

0The study of electric charges at rest and their electric fields and potentials0 Charges at rest if there is no net transfer of charge

A. Microstructure of Matter0 The smallest unit of matter is an atom

0Atoms are made up of protons, neutrons and electrons0 The electron is the fundamental negatively charged

particle of matter0 The proton is the fundamental positively charged particle

of matter

0The elementary charge (e) equals0 The charge on an electron (-e)0 The charge on a proton (+e)

0Because all atoms are electrically neutral, atoms contain equal number of protons and neutrons

0Neutrons have no charge

B. Charged Objects0Protons and neutrons cannot be removed from an

atom0Electrically charged objects are formed when neutral

objects gain or lose electrons0When an atom becomes a charged particle, it is called

an ion0 Excess electrons creates negative ions0 Loss of electrons creates positive ions0 Objects with the same sign of charge are repelled0 Objects with opposite signs are attracted

C. Transfer of Charge0 If a system only contains neutral objects, the total net

charge is zero0 If the objects are rubbed together, electrons are

transferred0The system as a whole remains neutral

Example3 spheres have initial charges

0When R and S touch, excess electrons (-8e) move to neutral (0e)0 When separated each sphere “splits” the excess

0 (-8e + 0e) ÷ 2 spheres0 Each sphere becomes -4e

0When S and T touch, excess electrons (-4e) moves to (+6e)0 When separated each sphere “splits” the excess

0 (-4e + 6e) ÷ 2 spheres0 Each sphere becomes +1e0 TOTALS R = -4e S = +1e T = +1e

0e R

-8e S

+6e T

D. Quantity of Charge0SI unit of charge is a coulomb (C)

0 1C = 6.25 x 1018 elementary charges (electrons)0The charge on an electron (-e) = 1.6 x 10-19C

0 The net charge on a charged object is always a multiple of the charge on an electron

E. Coulomb’s Law0The electrostatic force between 2 charges is

0 Directly related to the product of the charges0 Inversely related to the square of the distance between

them

0F…electrostatic force (newtons)0q…charge (coulombs)0r…distance between charges (meters)0k…electrostatic constant (8.99 x 109 N m2/C2)

F = kq1q2

r2

II. Electric FieldsoRegion around a charged particleoExerts a force on other charged particles

oRepresented by field linesoDirection a positive charge(+) would move

oIf lines are curved, charge would move tangent to the point on the field line

oBegin (+) and end (-)oNever cross

oEnergy varies inversely squared with distance

oStrength

Where E = electric field strength (N/C)F = force the charge experiences (N)q = the charge (C)

E = Fq

What is the magnitude of the electric field at a point in a field where an electron experiences a 1.0 N force?

E = 6.3 x 1018 N/C

E = Fq

E = 1.0 N1.60 x 10-19C

A. Potential DifferenceoWork done as charge is moved against a

field

oWhere W is work in joulesoq is charge in coulombsoV is potential difference

o Joules/coulomb is the derived unit volto 1 J/C = 1 volt

oIf the charge is an elementary charge (ex.

electron) the potential difference is an electron volt (eV)

o1 eV = 1.60 x 10-19J

V = Wq

Moving a point charge of 3.2 x 10-19 coulombs between two points in an electric field requires 4.8 x 10-18 joules. What is the potential difference between these two points?

V = 15 V

qV = W

3.2 x 10-19CV = 4.8 x 10-18 J

III Electric Current

A. Electric currentoThe rate that a charge passes a point in a circuitoRepresented using the symbol, IoUnit is an ampere (A)oFormula I = q t

o I is current in amperesoq = charge in coulombso t = time in seconds

oCurrent is measured using an ammeter

B. Electric circuito The closed path that a charged particle moves alongo Potential difference is also needed for an electric

currento Supplied by

o Cell o Battery

oMeasured using a voltmeter

o Electron flow determines the direction of currentoA switch is used to make, break or change the

connections in a circuit

C. ResistanceoElectrical resistance (R) is the opposition of

electron flowoRatio of potential difference to current flow

oR = V I

oWhere oV = potential difference in voltsoI = current in amperesoR = resistance in volts per ampere• Ohm (Ω)represents 1 volt per

ampereoResistance is affected by temperature

A current of 0.10 amperes flow through a lamp connected to a 12.0-volt source. What is the resistance of the lamp?

I = 0.10 AV = 12.0 VR = V IR = 12.0 V 0.10 AR = 120 Ω

Factors Affecting ResistanceLength of Wireo Increasing length, increases the collisions of electrons

with atoms in the wireo Directly related

Thickness of Wireo Increasing thickness creates more spaces for electrons to

travel through, decreasing the resistanceo Inverse relationship with cross-sectional area

Resistivityo Characteristic of the materialo Good conductors have low resistivitieso As temperature increases, resistivity increaseso Values found in reference tables

Resistance of a WireR = ρL AWhere• R is resistance in ohms (Ω)• ρ is the resistivity in ohm-meters (Ω-m)• L is length in meters (m)• A is cross-sectional area in square meters (m2)

Determine the resistance of a 4.00-meter piece of copper wire that has a diameter of 2.00 mm at 20°C.

ρ copper = 1.72 x 10-2

L = 4.00 mDiameter = 0.002 mArea = πr2

Area = π(.001)2

Area = 3.14 x 10-6 m2

R = (1.72 x 10-2 x 4.00) 3.14 x 10-6

R =2.19 x 10-2 Ω

Resistor• Device to have a definite amount of resistance• Used to limit current flow• Provide a potential drop• Symbol

Electric PowerPower (P) = Work/timeUnitsWork,,,joulesTime secPower wattsElectrical power is the product of VISince V=IR thenP = I2R