Find out the expression for the potential energy of a system of three charges `q_(1), q_(2) and q_(3)` located respectively, at `r_(1), r_(2) and r_(3)` with respect to the common origin O.

Explanation

Let three point charges `q_(1), q_(2) and q_(3)` have position vectors `r_(1), r_(2) and r_(3)`.

Potential energy of the charges `q_(1) and q_(2)`
`U_(12)= (1)/(4pi epsi_(0)) .(q_(1)q_(2))/(|r_(12)|)`
`=(1)/(4pi epsi_(0)).(q_(1)q_(2))/(|r_(3)- r_(1)|)`
Similarly, `U_(23)= (1)/(4pi epsi_(0)) .(q_(2)q_(3))/(|r_(3)-r_(2)|)`
`rArr U_(13)= (1)/(4pi epsi_(0)) .(q_(1)q_(3))/(|r_(3)-r_(1)|)`
`therefore` Net potential energy of the system,
`U= U_(12) + U_(23) + U_(10)`
`U= (1)/(4pi epsi_(0)) [(q_(1)q_(2))/(|r_(2)-r_(2)|) + (q_(2)q_(3))/(|r_(3)-r_(2)|) + (q_(1)q_(3))/(|r_(3)-r_(1)|)]`