Electric Potential

The electric potential is the potential energy per coulomb:

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

measured in volts ($1\ \mathrm{V}$ = $1\ \mathrm{J/C}$). It is a number, not a vector.

Around a point charge:

$$V = k\,\frac{Q}{r}$$

Potentials of several charges simply add.

Moving a charge across a potential difference $\Delta V$ takes work:

$$W = q\,\Delta V$$

$1\ \mathrm{eV} = 1.6\times10^{-19}\ \mathrm{J}$: the energy an electron gains across $1\ \mathrm{V}$.