The electric charge per unit area is +s for plate 1 and –s for plate 2.The magnitude of the electric field associated with plate 1 is s/eo, and the electric field lines for this plate are as shown. When the two are placed parallel to one another, the magnitude of the electric field is

1. 2s /eo between, 0 outside.2. 2s /eo between, ±s /eo outside.3. zero both between and outside.4. ±s /eo both between and outside.5. none of the above.

Conductors in Electrostatic Equilibrium• Conductors – materials with excess free electrons which allow charge to be easily

transferred throughout the object.• Free electrons – these are electrons that are not bound to atoms, but free to travel

throughout the materialInsulators have their electrons either weakly or strongly bound to their atoms, which means more work needs to be done to move the electrons around.

What would happen to a conductor placed within an external electric field?

• The electric field polarizes the conductor (instantaneously separates positive and negative charges)

What is the electric field inside the conductor?

• Zero – electric field inside conductor neutralizes the external electric field

The Electric field inside a conductor is always zero!!

E

If the electric field inside a conductor is zero and all charges have an electric field, where are all the excess charges located for a conductor?

• All excess charges are located on the outer surface of a conductor.

Verify using Gauss’s Law:

0

enclqE dA

0

enclqE

A

E can only be zero if qencl is zero!

What is the strength of the electric field generated by the surface charge of a conductor?

0

enclqE dA

0

enclqE

A

0

AE

A

0

E

•The electric field of a conductor is always s/e0 and directed perpendicular to the surface of the conductor (parallel to the area vector)

E

CH 23: Electric potential

If we have a positive charge q in an external electric field that we would like to move in a direction opposite to the direction of the electric field, what do we do?

B A

EF

• A force must be applied to the charge in order to move it from point A to point B against the force that the external electric field would normally apply to the charge.

What do we call it when we apply a force to an object in order to move it a certain distance?

• Work – we do work on the charge to store potential energy

Remember: W F ds W qE ds

Force we are acting against

This is similar to lifting an object off the ground against gravity!

Also recall that work is a change in the potential energy of a system.

U W

We can now relate work to potential energy and hence electric field to potential energy.

B

B A

A

U U U q E ds DU – change in potential energy (J)

UA – potential energy at point A (J)

UB – potential energy at point B (J)

E – external electric field (N/C)

q – charge external electric field is acting on (C)

s – path charge is being moved along (m)

Potential energy is a scalar quantity and does not depend on path (no direction).

When dealing with real charge systems containing more than one charge it is often more convenient to discuss the potential energy per unit charge.

UV

q f, V – electric potential

U – potential energy

JV V

C V is volts

Electric potential and electric potential energy are NOT the same!!

In order to move a charge between two points at different electric potentials you must change the potential energy of the system.

If you want to move a charge between two points at the same potential, how much must you change the potential energy by?

Zero – if you do not move between two different potentials you do not have to change the potential energy. No work is required.