Four point charges Q , q Q and q are placed at the corners of a square of side 'a' as shown in the Fig. Find the
potential energy of this system .

Explanation

The potential energy of the system
`U = (1)/(4pi in_(0)) [ (q_(A) q_(B))/(a) + (q_(A) q_(C))/(asqrt2) + (q_(A) q_(D))/(a) + (q_(B) q_(C))/(a) + (q_(B) q_(D))/(a sqrt2) + (q_(C) q_(D))/(a)]`
`= (1)/(4 pi in_(0)) [ (qQ)/(2) + (Q^(2))/(a sqrt2) + (qQ)/(a) + (qQ)/(a) + (q^(2))/(asqrt2) + (qQ)/(a)]`
`(1)/(4pi in_(0)) [ (4qQ)/(a) + ((Q^(2) + q^(2)))/(a sqrt2)] = (1)/(4 pi in_(0) a) [4 qQ + ((Q^(2) + q^(2)))/(sqrt2)]`