Suppose we have a negative point charge with charge $-Q$. What is the electric potential at a point $P$, which is a distance $R$ from the point charge?

• The charge with value $-Q$ is a point charge.
• The point $P$ is a distance $R$ away from the point charge.

• The electric potential at $P$.

• The electric potential at $P$ is due entirely to the point charge.
• The electric potential infinitely far away from the point charge is $0 \text{ V}$.

• The electric potential from the point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents our charge ($-Q$) and $r$ is our distance ($R$).

The electric potential at $P$ is given by \begin{align*} V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ &= \frac{1}{4\pi\epsilon_0}\frac{(-Q)}{R} \\ &= -\frac{1}{4\pi\epsilon_0}\frac{Q}{R} \end{align*}