**Electric potential energy**

Electric potential energy is the energy a charge has due to its position relative to other charges. If you take a ball with mass m and raise it to any height, you are giving it gravitational potential energy.

Let a test charge q_{0} be at rest between two oppositely charged plates [Figure]. Since the plates are charged, the test charge will be attracted by the lower plate. Let the test charge be kept to rest at the position. A by applying some external force (say by hand). Now, let the charge be taken from position A to position B against the attractive force by applying some external force. The external force does work in taking the charge from A to B. According to work-energy principle, the work done is equal to the change in total energy.

Now, at positions A and B the body, is at rest, so there will be no change in kinetic energy; only change in potential energy will take place. Since the phenomenon is electrical, so the associated potential energy is called electrical potential energy. Now according to work-energy theorem work done W_{AB} is equal to charge in electrical potential energy. That is-

W_{AB} = E_{B} – E_{A}

Here E_{B} and E_{A} are the electric potential energy at point B and A respectively. Since electric force is a conservative force, so work done W_{AB} in taking the test charge from A to B is independent of the path i.e., W_{AB} will be same for any path. As the electric force resisting the motion of the test charge is dependent on the amount of charge [since F = Eq_{0}], so work done in taking the test charge from points A to B depends on the amount of charge. Hence, it is convenient to consider work done for unit charge. Hence work done per unit charge.

W_{AB}/q_{0} = (E_{B} – E_{A}) / q_{0} = (E_{B} / q_{0}) – (E_{A} / q_{0})

This potential energy per unit charge is called electric potential or simply potential.

W_{AB}/q_{0} = V_{B} – V_{A}

Here, V_{B} and V_{A} are respectively the potentials at point B and A.