Three charges are placed along x- axis at `x = -a , x=0` and `x=a` as shown . Calculate the potential energy of the system.

Explanation

The potential energy of two point charges separated by a distance r is given by U = `(q_(1)q_(2))/(4 pi epsilon_(0)r)` in the given arrangement , there are three unique pair of charges,
`U_(1) = (q^(2))/(4 pi epsilon_(0)a) , U_(2) = (q^(2))/(4 pi epsilon_(0)a) , U_(3) = (q^(2))/(4 pi epsilon_(0)(2a))`
`therefore` total potential energy U = `U_(1) + U_(2) + U_(3)`
`rArr U = (q^(2))/(4 pi epsilon_(0)) [ (1)/(a) + (1)/(a) + (1)/(2a)] `
`rArr U = (5q^(2))/(8 pi epsilon_(0) a)`