Potential in a Uniform Field

Summary: in a uniform electric field the change in potential is:

DV =
DU
q
=
qEDd
q
= E Dd

where Dd is the component of the displacement in a direction opposite to the field.

This is analogous to the change in gravitational potential for an object with mass:

DV =
DU
m
=
m g h
m
= g h

Note that what is really important is not the value of the potential at any point, but the change in potential experienced by an object as it moves from one point to another. That change in potential is directly related to the object's change in potential energy.

The simulation shows the equipotentials for a uniform field. In which direction is the field?

  1. Up
  2. Down
  3. Left
  4. Right
  5. There is not enough information to decide














Let's say a +q test charge is moved horizontally a distance r. What is the change in potential experienced by this charge?

  1. Zero
  2. +kq/r
  3. -kq/r
  4. +12 volts
  5. -12 volts














Now the +q test charge is moved vertically a distance r. What is the change in potential experienced by this charge now?

  1. Zero
  2. +kq/r
  3. -kq/r
  4. +12 volts
  5. -12 volts














How would your answer change if the charge had been a negative charge, -q, instead?

  1. The answer would not change
  2. The answer would flip sign














Consider two cases. In case 2 the equipotential lines are twice as far apart as they are in case 1. In this simulation each line differs from neighboring lines by 2 volts. If a +q test charge is moved vertically a distance r in both cases, in which case does it experience the largest change in potential energy?

  1. Case 1
  2. Case 2
  3. Equal in both cases
  4. The change in potential energy is zero in both cases














In which case is the electric field strongest?

  1. Case 1
  2. Case 2
  3. Equal in both cases
  4. Can not be determined from the information given