Question

Equal charges of 3.00x10^-9 C are situated at the three corners of a square of side 5.20 m. Find the potential at the unoccupied corner.

Answer 1

Electric potential created at distance $r$ from point charge $q$ is $\varphi = \frac{k q}{r}$, where $k = 9 \cdot 10^9 \frac{N m^2}{C^2}$ is Coulomb's constant. Electric potential created by multiple point charges is just the sum of potentials, created by each charge.

Hence, electric potential at the unoccupied corner is $\varphi = \frac{k q}{a} + \frac{k q}{a} + \frac{k q}{\sqrt{2} a} = \frac{k q}{a}(2+ \frac{1}{\sqrt{2}})$, where $a$ is the side of a square. Substituting $a = 5.2 m$ and $q = 3 \cdot 10^{-9} C$, obtain $\varphi \approx 14.06 V$.