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Electric potential

Electric fields describe force per unit charge. Electric potential describes electric potential energy per unit charge.

If a charge $q$ at a point has electric potential energy $U$, the potential is

$$V=\frac{U}{q}.$$

The SI unit is the volt:

$$1,\mathrm V=1,\mathrm{J/C}.$$

Potential difference

Only differences in potential affect energy changes. Moving a charge between points $A$ and $B$ changes its electric potential energy by

$$\Delta U=q\Delta V=q(V_B-V_A).$$

A positive charge tends to move toward lower potential when only the electric force acts; a negative charge behaves oppositely because of the sign of $q$.

Point charge

Choosing zero potential infinitely far away, a point charge $Q$ produces

$$V(r)=\frac1{4\pi\varepsilon_0}\frac{Q}{r}.$$

Potential is a scalar, so contributions from several source charges add algebraically:

$$V=\sum_i V_i.$$

Voltage

In circuit language, a potential difference is commonly called a voltage. A voltage tells how much electric potential energy changes per unit charge between two points.