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

In this situation, the centripetal force is provided by he electrostatic force of attraction
(i) By newton's second law, F = `(1)/(4 pi epsilon_(0))(q^(2))/((2R)^(2)) = (mv^(2))/(R )`
`rArr " " v = sqrt((1)/(4 pi epsilon_(0))(q^(2))/((4R)m))`
(ii) Kinetic energy of the system = `(1)/(2) mv^(2) + (1)/(2) mv^(2) = (q^(2))/(4 pi epsilon_(0)(4R)) = (q^(2))/(16 pi epsilon_(0)R)`
(iii) Potential energy of the system = `(1)/(4 pi epsilon_(0)) (q(-q))/(2R ) = (-1)/(4 pi epsilon_(0)) (q^(2))/((2R)) = (-q^(2))/(8pi epsilon_(0)R)`
(iv) Total energy of the system = K.E + P.e = `(-q^(2))/(4 pi epsilon_(0)(4R)) = (-q^(2))/(16 pi epsilon_(0)R)`