Question

A square is 1.0 m on a side. Point charges of +4.0 µC are placed in two diagonally opposite corners. In the other two corners are placed charges of +3.0 µC and -3.0 µC. What is the potential (relative to infinity) at the midpoint of the square?

Answer 1

Answer:

$V = 1.44\times 10^{5}~V$

Explanation:

The electric potential can be found by using the following formula

$V = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}$

Applying this formula to each charge gives the total potential.

$V = V_1 + V_2 + V_3 + V_4\\V = \frac{1}{4\pi\epsilon_0}\frac{4\times 10^{-6}}{(\sqrt{2}/2)^2} + \frac{1}{4\pi\epsilon_0}\frac{4\times 10^{-6}}{(\sqrt{2}/2)^2} + \frac{1}{4\pi\epsilon_0}\frac{3\times 10^{-6}}{(\sqrt{2}/2)^2} - \frac{1}{4\pi\epsilon_0}\frac{3\times 10^{-6}}{(\sqrt{2}/2)^2}\\V = \frac{16\times 10^{-6}}{4\pi\epsilon_0}\\V = 1.44\times 10^{5}~V$

Since the potential is a scalar quantity, it is safe to sum all the potentials straightforward. And since they all placed on the corners of a square, +3 and -3 μC charges cancel out each other.