Derive an expression for electric potential energy of a system of charges in an electric field.

Explanation

Consider point charges `q_(1),q_(2),q_(3)` Let `r_(12),r_(23),r_(31)` be the distances between `q_(1),q_(2),q_(2),q_(3),q_(3),q_(1)` respectively. The potential energy between `q_(1)&q_(2)` will be
`U_(1)=(1)/(4piepsi_(0)).(q_(1)q_(2))/(r_(12))` as proved above.
Similarly, `U_(2)-(1)/(4piepsi_(0)).(q_(2)q_(3))/(r_(23))` between `q_(2) and q_(3)`
and `U_(3)=(1)/(4piepsi_(0)).(q_(3)q_(1))/(r_(31))`.