Four charges $+q, -q, +q, -q$ are arranged at the corners of a square ABCD of side $d$. A charge $q_

Question

Four charges $+q, -q, +q, -q$ are arranged at the corners of a square ABCD of side $d$. A charge $q_0$ is brought to the centre E of the square. How much extra work is needed to do this?

Professor PC Thomas Classes · Answer

The potential at the center of the square due to the four charges is $V = k(\frac{q}{r} + \frac{-q}{r} + \frac{q}{r} + \frac{-q}{r}) = 0$. Since the potential at the center is zero, the extra work needed to bring $q_0$ there is $W = q_0 V = 0$.