D.2.13 (HL)—Electric potential as scalar

Define electric potential

Electric potential $V_e$ at a point is the work done per unit positive test charge in bringing it from infinity to that point. Its unit is $\mathrm{J\,C^{-1}}$, equivalent to volts. Set $V_e=0$ at infinity.

Add potentials algebraically

Electric potential is a scalar, so contributions from several point charges add with their signs:
$$V_e=\sum_i k\frac{Q_i}{r_i}$$
There is no vector-angle calculation when combining potential values.

Interpret the result

A positive source contributes positive potential and a negative source contributes negative potential. A point can have zero net potential because positive and negative contributions cancel, even though the electric field there is not necessarily zero.

Common trap

Do not add electric field magnitudes as though they were scalar, and do not infer zero electric field from zero potential. Potential and field are different quantities.