Physics - Electrostatics Question with Solution | TestHub

Let the charge magnitude be q and the distance from O be d. The interaction energy sums 4 adjacent pairs (distance $d\sqrt{2}$) and 2 opposite pairs (distance 2d).

In case D the four adjacent terms cancel in pairs, and the two opposite-pair terms $-\frac{k{q}^2}{2d}$ and $+\frac{k{q}^2}{2d}$ also cancel, giving U = 0.

Cases A, B and C each leave a nonzero signed sum, so the total interaction energy is zero only in case D.