Question

How much work done to assemble eight identical point charge

Answer 1

Your question is incomplete .
A complete question is ------> how much work is done to assemble 8 identical point charges,each of magnitude q,at the corners of a cube of side a?

solution :- we have to find potential energy in cube .
in cube , we have ,
12 edges of length a , 12 side diagonals of length a√2 and 4 body diagonals of length a√3
so, potential energy = [ 12kq²/a + 12kq²/a√2 + 4kq²/a√3 ]
P.E = 4kq²/a [ 3 + 3/√2 + 1/√3 ]
= 4kq²/a [ 3√6 + 3√3 + √2]/√6
=4kq²/a√6 [ 3√6 + 3√3 + √2] Joule

∴ Workdone = potential energy
= 4kq²/a√6 [3√6 + 3√3 + √2]