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 separate by a distance r is givenb y `U = ( q_(1) q_(2))/( 4pi epsilon _(0)r)`
In the given arrangement, there are three unique pair of charges.

`U_(1) = ( q^(2))/( 4pi epsilon_(0)a), U _(2) = ( q^(2) )/(4pi epsilon_(0)a), U_(3) = (q^(2))/(4pi epsilon_(0)(2a))`
`:. ` Total potential energy `U = U_(1) + U_(2) + U _(3)`
`implies U = ( q^(2))/( 4pi epsilon_(0))[(1)/(a) + (1)/(a) + (1)/(2a)]`
`implies U = ( 5q^(2))/( 8 piepsilon_(0)a)`