Find the electric potential energy of the system of charges.
(a)

Explanation

(a) Number of pairs `= 3`
`U = (1)/(4 pi in_(0)) .[(15 Q.Q)/(3d) + (8Q.Q)/(4d) + (15 Q . Q)/(5d)]`
`= (1)/(4 pi in_(0)).(31 Q^(2))/(d)`
(b) Number of pairs `= (4(4 - 1))/(2) = 6`
`AC = BD = sqrt(2) d`
`U = (1)/(4 pi in_(0)) [(Q . Q)/(d) xx 4 + (Q.Q)/(sqrt(2) d) xx 2]`
`= (1)/(4 pi in_(0)) (Q^(2))/(d) [ 4 + sqrt(2)]`