Electricity and Magnetism Electric forces hold atoms and

molecules together. Electricity controls our thinking, feeling,

muscles and metabolic processes. Electricity and magnetism underpin much of our current technology (e.g. computers). Electricity and magnetism are linked on a fundamental level.

Electric Charges• Evidence for electric charges is everywhere, e.g.

– static electricity.– lightning.

• Objects may become charged by contact and frictional forces.

• Benjamin Franklin (1700’s) discovered that there are two types of charges:– positive charge.– negative charge.

• Franklin also discovered that like charges repel and unlike charges attract one another.

• Electric charge is– quantized (Millikan)– conserved (Franklin)

Electric Charges in Atoms• Atoms consist of a nucleus

containing positively charged protons.

• The nucleus of an atom is surrounded by an equal number of negatively charged electrons.

• The net charge on an atom is zero.

• An atom may gain or lose electrons, becoming an ion with a net negative or positive charge.

• Polar molecules have zero net charge but their charges are unevenly distributed in space (e.g. water).

Nuclear diameter ~ 10-15 m (femtometer)

Atomic diameter ~ 10-9 m (nanometer)

Classes of Materials• CONDUCTORS are materials in which

charges may move freely (e.g. copper).

• INSULATORS are materials in which charges cannot move freely (e.g. glass).

• SEMICONDUCTORS are materials in which charges may move under some conditions (e.g. silicon).

Charges and the Earth

• The earth acts as a near-infinite source or sink of charges, and therefore its net charge cannot easily be changed.

• Any conductor in contact with the earth is said to be GROUNDED and cannot receive a net charge. (principle of lightning rod)

Induced Charge• Charged objects brought close to a conductor may

cause charge to redistribute (polarize the conductor).

• If a polarized conductor is momentarily grounded, charge will be transferred to/from the earth, and it may be left with a net charge (by INDUCTION).

• Objects may be charged by– conduction (requires contact with another

charged object.– induction (requires no contact with another

charged object).

Electric Force and Coulomb’s Law• If two point charges q1 and q2 are separated

by a distance r, the magnitude of the electric force Fe between them is:

221

r

qqkFe

where k = 8.99 x 10 9 N m2/C2 is the Coulomb constant, q1 and q2 are in Coulombs (C), r is

in meters (m) and Fe is in Newtons (N).

Quantum of Electric Charge

• Electric charge is quantized. The smallest possible unit is the charge on one electron or one proton: e= 1.602 x 10-19 Coulombs

• No smaller charge has ever been detected in an experiment.

Electric Force Vector

• The force on a point charge q1 exerted by another point charge q2 separated by a distance r21 is:

. and joining

axis thealongr unit vecto a is ˆ where

ˆ

12

21

122121221

2112

qq

r

FFrr

qkqF

Principle of Superposition

• For a system of N charges q1, q2, q3, …, qN,

the resultant force F1 on q1 exerted by charges

q2, q3, …, qN is:

NFFFF 113121

• Each charge may be considered to exert a force on q1 that is independent of the other

charges present.

Field Forces and Electric Field

• Field forces act through space even if there is no contact (e.g. gravitational force).

• The ELECTRIC FIELD E is defined in terms of the electric force that would act on a positive test charge q0 :

N/Cin 0q

FE e

Electric Field• The electric force on a positive test charge q0

at a distance r from a single charge q:

rr

qqkFe ˆ

20

• The electric field at a distance r from a single charge q:

rr

qk

q

FE e ˆ

20

EqFe

0

Electric Field due to a Group of Charges:

ii i

i rr

qkE ˆ

2

0i tofromr unit vecto a is ˆ q qri

Example ProblemFour point charges are at

the corners of a square of side a as shown.

a) Determine the magnitude and direction of the electric field at the location of q.

b) What is the resultant force on q?

2q q

4q3q

a

a

a

a

Electric Field from Continuous Charge Distributions

• If a total charge Q is distributed continuously, it may be sub-divided into elemental charges dQ, each producing an electric field dE:

22

r

dQkdEE

r

dQkdE

02

02 4

1 ˆ

4

1ˆ

πεkr

r

dQr

r

dQkE

ε0 = permittivity of free space

Uniform Charge Distributions

• Volume Charge Density: ρ=Q/V• Surface Charge Density: σ=Q/A• Linear Charge Density:λ=Q/l

Example:• A continuous line of charge lies along the x-

axis, extending from x=x0 to positive infinity. The line carries a uniform linear charge density λ0. What are the magnitude and direction of the electric field at the origin?

Example Problem: Electric Field due to a Power Line

• A power line is suspended a constant distance yo above the ground, and carries a uniform linear charge density λo. Assume that the wire is infinitely long and that the ground is a flat plane. What are the magnitude and direction of the electric field on the ground immediately below the power line?

Electric Field LinesElectric Field Lines:• describe the direction of the electric field at any point• The density of field lines is proportional to the

magnitude of the electric field.• The directions of arrows indicate the direction of the

force on a positive test charge.

• Rules:– Lines begin on + charge and end on – charge– Number of lines approaching or leaving a charge

is proportional to the magnitude of the charge.– Electric field lines may never cross.

Electric Field Lines: Conventions Positive Point Charge Negative Point Charge

Electric Field lines