I. Set up a uniform E-field by placing two parallel plates close to each other and putting equal, but opposite, charges on them. The work done by the E-field in moving a (+) charge from point A to point B is

dW_{A to B} = **F ^{.} **d

**
**dW_{A to B}** = **q_{0 }**E ^{.}
**d

A. Recall that the work done by a conservative force is the negative of the change in potential energy

Work = -(change in U)

W_{A to B }= -(U_{B} - U_{A})

B. The E-field is a conservative field - the work done is independent of path.

C. Here the E-field is constant. If it is not constant, we have to use

dU = -dW = - q_{0 }**E ^{.} **d

and integrate from A
to B.

Let's look at this for a point charge.

II. The electrostatic potential is the potential energy per unit charge

V = U/q

A. How is potential difference related to the E-field?

B. What is an equipotential surface?

III. What is a potential gradient?

IV. Notes on Potentials and Conductors

A. No work is needed to move a charge between two points at the same potential.

B. The surface of a conductor is a constant potential surface.

C. The electrostatic potential is constant inside a conductor and equal to its value at the surface.

D. The electron-volt is a unit of energy.