Consider a regular cube with charge +Q at every corner except one corner, where the charge is -Q. The distance from every corner to the centre P is r. If the electric-field magnitude at P is E = nkQ/r², find n.

Question

G1 Physics · Accepted Answer

If all eight corners carried +Q, the net field at the centre would be zero by symmetry. Changing one corner from +Q to -Q is equivalent to adding an extra charge -2Q at that corner. Therefore E = 2kQ/r². Comparing with E = nkQ/r² gives n = 2.