ELECTROSTATIC POTENTIAL

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

                       dWA to B = F . ds

                       dWA to B  = q0 E . ds
 
 
 
 
 
 
 
 
 
 
 
 

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

                     Work = -(change in U)

                     WA to B = -(UB - UA)

  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 = - q0 E . ds

     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.