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))/(4 pi epsilon_(0)r)` where r is the separation between the charges .

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