Determine the interaction energy of the point charge located at the corners of a square with the side a in the circuits shown in figure.

Explanation

Interaction energy of any two point charges `q_(1)` and `q(2)` is given by `( q_(1) q_(2))/( 4pi epsilon_(0))` where r is the separation between the charges.

Hence, interaction energy of the system .
`U_(a) = 4(q^(2))/( 4pi epsilon_(0)a)+2(q^(2))/( 4pi epsilon_(0)(sqrt(2)a))`
`U_(b) = 4(-q^(2))/( 4pi epsilon_(0)a)+2(q^(2))/( 4pi epsilon_(0)(sqrt(2)a))`
and `U_( c) = 2 ( q^(2))/( 4pi epsilon_(a)) - ( 2q^(2))/( 4pi epsilon_(0)a) - ( 2q^(2))/( 4pi epsilon_(0)( sqrt(2)a)) = ( sqrt(2) q^(2))/( 4pi epsilon_(0)a)`