## Electric potential (energy)

Electric potential energy is similar to gravitational potential energy, except it can be positive or negative since the electric force can repel as well as attract. Electric potential energy is given by the formula

E_"el" = k(q_1q_2)/r.

From this we can derive a formula for a change in electric potential energy:

Delta E_"el" = kq_1q_2(1/r_2 - 1/r_1).

Electric pontential is, confusingly, not the same as electric potential energy. While the latter is measured in joules, electric potential is measured in joules per coulomb. It represents the E_"el" that a unitary point charge would have at a particular point. It is denoted with V and calculated with

V = E_"el"/q_2 = (kq_1)/r.

V is to E_"el" as vec epsilon is to F_"el". They differ only by an r in the denominator:

|vec epsilon| = V/r.

Most of the time, we talk not about electric potential but about electric potential difference, also known as voltage:

Delta V = kq(1/r_2 - 1/r_1).

In general, we can relate work to voltage with

W = Delta E_"el" = q_2Delta V.

For parallel plates, we have a more specific equation. The work done by the electric force to move a charge q_2 from one plate to the other is given by

W = Delta E_"el" = q_2|vec epsilon|d,

where d is the distance between the plates in metres (m). Why were we able to replace Delta V by |vec epsilon|d? Because, for parallel plates,

|vec epsilon| = (Delta V)/d.

This is not true for point charges. It looks similar to the general equation |vec epsilon| = V//r mentioned above, but that Delta  makes a big difference. With point charges, the amount of work done is strictly related to the values of r_1 and r_2. Not so with parallel plates—since the electric field is uniform, it doesn’t matter where the particle is between the plates.