Two charges `+q and -q`, each of mass m, are revoloving in a circle of radius R, under mutal electrostatic force, Find (i) speed of each charge (ii) kinitic energy of the system (iii) potental energy of the system and (iv) total energy of the system.

Explanation

The charges `+q and -q` revolve around their center of mass O with same angular velocity. As their mass is same, their speed (v) will be same as shown in Fig.

(i) The centripetal force required is provided by the electrostatic force of attraction between the two particles.
`:. (mv^(2))/(R ) = (1)/(4pi in_(0)) (q xx q)/(R + R^(2))`
`v = sqrt((q^(2))/(16 pi in_(0) mR))`
(ii) Kinectic energy of the system of two particles
`K = 2xx (1)/(2) mv^(2) = mv^(2) = (m xx q^(2))/(16pi in_(0) mR) = (q^(2))/(16pi in_(0) R)`
(iii) Potential energy of the system
`U = (q(-q))/(4pi in_(0) (R + R)) = (q^(2))/(8pi in_(0) R)`
(iv) Total energy of the system
`E = K + U = (q^(2))/(16 pi in_(0) R) - (q^(2))/(8pi in_(0) R)`
`E = (q^(2))/(16pi in_(0) R)`