Identical 2.5 µC charges are located on the vertices of a square with sides that are 1.0 m in length. What is the electric potential (relative to zero at infinity) at the centre of the square?

Question

Quizplus · Accepted Answer

The electric potential due to a point charge is given by $V = \frac{kq}{r}$, where $V$ is the potential, $k$ is Coulomb's constant ($9 \times 10^9 \, \text{Nm}^2/\text{C}^2$), $q$ is the charge, and $r$ is the distance from the charge to the point of interest. Since the charges are identical and located symmetrically around the center of the square, their potentials at the center add up. The distance from any corner to the center of the square is $\frac{\sqrt{2}}{2}$ meters (diagonal of the square divided by 2, using Pythagoras). The total potential is thus $4 \times \frac{kq}{r}$, with $q = 2.5 \times 10^{-6}\, \text{C}$ and $r = \frac{\sqrt{2}}{2}\, \text{m}$. Substituting the values gives a positive potential, matching choice A.