Relationship Between Electric Potential Energy and Work If you gain electric potential energy, is the magnitude of the EPE equal to the work done by the particle in the electric field? Or is the magnitude of the EPE equal to the work done on the particle?
 A: Assuming the charge begins and ends at rest, or moves between two points at constant velocity so that there is no change in kinetic energy, then the increase in the magnitude of the EPE is equal to the work done on the charge by an external agent against the direction of the electric field. An example is a battery that does work (converts chemical energy to electrical potential energy) to separate charge at its terminals increasing the electrical potential and electrical potential energy of the charge.
Under the same assumption, a decrease in the magnitude of the EPE is equal to the work done by the electric field on the particle. An example is the work done by an electric field moving charge through a resistor in a circuit. There is a drop in voltage (drop in electrical potential) across the resistor.
Hope this helps.
A: If the particle gains electric potential energy, work must be done on the particle by some external force, or some other energy source, such as kinetic energy, must be converted to electric potential energy.
If the particle loses electric potential energy, work is done on the particle by the electric field.
Think of rolling a boulder up a hill. Work is done by you to push it up there, and work is said to be done on the boulder if you let it roll back down (gravity is doing the work here).
