Derive an expression for potential energy of a system of three charges in the absence of external electric field.

Explanation

Consider point charges `q_(1),q_(2),q_(3)` let `r_(12),r_(23),r_(31)` be the distance between `q_(1),q_(2),q_(3),q_(1)` respectively the potential energy between `q_(1)` & `q_(2)` will be
similary `U_(2)=(1)/(4 pi epsilon_(0)).(q_(2)q_(3))/(r_(23))` between `q_(2)` and `q_(3)`
totoal energy of the system as a result of assembiling the charge `U=U_(1)+U_(2)+U_(3)`
`U=(1)/(4pi epsilon_(0))(q_(1)q_(2))/(r_(12))+(q_(2)q_(3))/(r_(23))+(q_(3)q_(1))/(r_(31))`