Electricity and Magnetism

Underlying a Whole Lot of Phenomena

Outline

• Stationary charges– forces, potential, fields

• Moving charges– current, resistance, circuits

• Magnetism– another effect of moving charges

• Magnetic Induction– Pushing charges with magnetism

Electric Charge

The Electric Force

Coulomb’s Law

F =

k = 8.992 109

C = coulomb (unit of electric charge)

kq1q2

d2

Nm2

C2

Coulomb’s Law

F =

Force is attractive for opposite charges

Force is repulsive for like charges

kq1q2

d2

The electric force is like the gravitational force because

a. Opposites attract.b. Both decrease as 1/d2.c. Both involve charge.d. Both were identified by Isaac Newton.e. All of these.

Discussion Question

The electric force is different from the gravitational force because

a. Gravity is only attractive.b. The electric force is much stronger.c. Electric charges can cancel.d. All of the above.

Discussion Question

Example Problem

The electron has a charge of –1.6 10-19 C and the proton has a charge of 1.6 10-19 C. Their average separation in a hydrogen atom is 5.3 10–11 m. What is the force between them at this distance?

What is the force between the electron and proton of a hydrogen atom when the electron is twice as far away?

a. Twice as much.b. The same.c. Half as much.d. One fourth as much.

Quick Question

Charge Polarization

tells us something about matter

Scenario

A bag contains equal numbers of positive and negative charges. The charges can move around inside the bag, but they cannot leave the bag. The bag is placed near a very large, immobile + charge.

++–

+–

+–

+

–

Quick Question

What sort of force exists between the + charges in the bag and the large + charge?

++–

+–

+–

+

–

A. The + charges are attracted to the charge.

B. The + charges are repelled by the charge.

C. The + charges are neither attracted nor repelled.

Quick Question

What sort of force exists between the – charges in the bag and the large + charge?

++–

+–

+–

+

–

A. The – charges are attracted to the charge.

B. The – charges are repelled by the charge.

C. The – charges are neither attracted nor repelled.

Quick Question

In which direction do the + charges in the bag accelerate due to the large + charge?

++–

+–

+–

+

–

A. Toward the charge.

B. Away from the charge.

C. The + charges will not accelerate.

Quick Question

In which direction do the – charges in the bag accelerate due to the large + charge?

++–

+–

+–

+

–

A. Toward the charge.

B. Away from the charge.

C. The – charges will not accelerate.

Poll Question

After the charges re-distribute, which force to the external + charge will be stronger?

++

–+

–

+

–+

–

A. The attraction to the – charges.

B. The repulsion to the + charges.

C. The attraction and repulsion will exactly cancel.

Poll Question

What sort of force exists between the bag overall and the large + charge?

+

A. The bag is attracted to the charge.

B. The bag is repelled by the charge.

C. The bag is neither attracted nor repelled.

+

–+

–

+

–+

–

Group Poll Question

What sort of force on the bag will exist if the external charge is negative?

–+–

+–

+–

+

–

A. The bag is attracted to the charge.

B. The bag is repelled by the charge.

C. The bag is neither attracted nor repelled.

Coulomb’s Torsion Balance

Principle of Superposition

Force from several charges = sum of forces from individual charges

a

b

d

c

Fb Fc

Fd

Fb

Fc

Fd

F

F = Fb + Fc + Fd

Vector Fields

Electric field

• Direction is the direction of the force exerted on a positive charge

• Vector arrows point away from positive charges and toward negative charges

• Magnitude is the force in N on a +1 C charge

Electric Field

Unit = N/C

Visualizing a Field

• Magnitude of the force on a charge is greater where field lines are close together

• Direction of the force is parallel to field lines– Force on a positive charge is along field lines– Force on a negative charge is opposite field

lines

Field Lines

Question

Particles A–D have the same charge. Which experiences the greatest force from the field? (Green arrows are field lines.)

A

B

C

D

Example

Draw field lines for the electric field about these two objects with opposite charges.

+ -

Group Work

Draw field lines for the electric field about these two objects with equal charges.

+ +

Electric Potential

What is the work required to move a charged object through a field?

Unit = J/C = V = volt

x

Electric Potential

Surfaces of Equal Potential

• Surfaces always perpendicular to electric field lines/vectors (why?)

• Potential changes rapidly where field is strong (why?)