Question

A regular hexagon of size 10 has a charge 5uc at each of it's vertices. Calculate the potential at it's center with answer

Answer 1

Let us assume, that the charge Q is placed at the centre of the square (having side a), so as to keep all the four charges in equilibrium. Clearly, charge Q has to be negative in nature to hold charges +q in equilibrium.

If the net force on a charge +q at any corner (say A) is zero, then by symmetry it follows that the net force experienced by the other charges at other corners will also be zero.

The problem is comprehensively solved here—

See the attachment

So the required charge Q (kept at the centre of the square)= -q (2√2+1) /4