Two charges, `+q` and -q, each of mass m , are revolving in a circle of radius R, under mutual electrostatic force. Find (i) speed of each charge (ii) kinetic energy of system (iii) potential energy of the system (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)`