Derive the expression for the potential energy of a system of point charges.

Explanation

(i) The electric potential at a point P due to a collection of charges `q_(1),q_(2),q_(3),...q_(a)` is equal to sum of the electric potentials due to individual charges.
`V_("tot") =(kq_(1))/(r_(1))+(kq_(2))/(r_(2))+(kq_(3))/(r_(3))+...(kq_(n))/(r_(n))=(1)/(4 pi epsi_(0))sum _(i=1)^(n)(q_(i))/(r_(i))`
(ii) where `r_(1),r_(r),r_(3),......r_(n)` are the distance of `q_(1),q_(2),q_(3),....q_(n)` respectively from P (Figure).