Determine the interaction energy of the point charges located at the corners at the corners of a square with the side `a` in the circuit shown in Fig.

Explanation

(a) Interaction energy of any point chagres `q_(1)` and `q_(2)` is given by `(q_(1) q_(2))/(4pi epsilon_(0) r)` 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) q) + 2 (q^(2))/(4pi epsilon_(0) (sqrt(2) a))`
and `U_(e) = 2 (q^(2))/(4pi epsilon_(0) a) - (2q^(2))/(4pi epsilon_(0) a) - (2q^(2))/(4pi epsilon_(0) (sqrt(2) a)) = (sqrt(2) q^(2))/(4pi epsilon_(0) a)`