Electric potential

Electric potential ($V$) is electric potential energy per unit Charge:

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

Its unit is the volt, where $1\mathrm{V}=1\mathrm{J}{\mathrm{C}}^{-1}$. Saying “this point is at 5 V” only makes sense relative to a chosen zero/reference point. Moving the zero of potential changes all potential values by a constant, but it does not change any physical prediction.

The physically important quantity in circuits is usually Voltage, the difference in electric potential between two points:

$\Delta V=V_b-V_a=\frac{\Delta U}{q}$

A positive charge naturally tends to move from higher potential energy toward lower potential energy. Electrons are negative, so their potential energy changes with the opposite sign from the electric potential.

Electric field around a large and a small conducting sphere at opposite electric potential. Purple represents highest potential, yellow near zero, and cyan lowest potential.

Connection to work: if an external agent slowly moves charge $q$ through a potential difference $\Delta V$, the work required is $W=q\Delta V$.

Common mistake: treating potential as an absolute height. Only differences in potential affect motion and energy transfer.