How is electric potential energy related to work and other kinds of potential energy?

Why is the water stored so high up? It took work to lift it up there. That work is stored as potential energy. When the water is allowed to flow down a pipe and out, it is moving fast because the potential energy has been converted to kinetic energy. Notice what matters here is the difference of the height at which it was stored and the height at which it is used.

Similarly, when charges have been separated, work was done. The stored energy is the electric potential energy difference.

Consider a whole field of water balloons. The ones thrown the highest will be moving the fastest when they come back down.

Water from the tank that was raised higher will be moving faster when it exits the pipe. Similarly, if we put more work into separating charges, we will give them greater potential energy. The charges with higher potential energy will move faster after letting them go, if everything else is held to be the same.

Check out these simulations of the electric field, showing lines of equal potential. Falstad E field simulation
ICPhysWeb simulation

A topographic map shows lines of equal elevation. We can think of this as lines of equal gravitational potential energy. Note that where the equipotential lines are closer together, the hillside is steeper. This denotes places where the potential changes more rapidly.

Massive particles gain kinetic energy when they undergo a loss of gravitational potential energy. The steeper the change, the more kinetic energy gained. For example, a block sliding down a steeper ramp will gain speed faster than a block sliding down a ramp that is less steep.

Charged particles similarly gain kinetic energy when they lose potential energy. There is an added complication due to the fact that there are positive and negative charges. Electrons gain kinetic energy when they undergo an increase in electric potential energy.

Electric potential

Recall that we defined the electric field as the electric force per charge. We will make a similar definition here for energy. We define the electric potential, V, as the electric potential energy per charge.

The unit of electric potential is joules per coulomb, also called volts. The potential difference between two points is called the voltage.

Sample question

An electron is released from rest at point B, where the potential is 0. Afterward, the electron

   A. remains at rest at B

   B. moves toward A at a constant speed

   C. moves toward A with increasing speed

   D. moves toward C at a constant speed

   E. moves toward C at an increasing speed

Force and potential energy

These quantities are calculated for/on charged particles. When dealing with force and potential energy, the r stands for the distance between the particles.

Field and potential

These quantities are calculated for locations in space. For field and potential, the r stands for the distance from the charge to the place where the quantity is being calculated.

Switching from field to potential is essentially the same as switching from force to potential energy.

To switch from potential to field, reverse the process.