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 the electrostatic force of attraction.
(i) By Newton's second law, `F = (1)/( 4pi epsilon_(0)(2R)^(2)) = ( mv^(2))/(R ) `
`implies v= sqrt((1)/(4pi epsilon_(0))(q^(2))/((4R)m))`

(ii) Kinective energyof the system `(1)/(2) mv^(2) + (1)/(2)mv^(2) = ( q^(2))/(4pi epsilon_(0)(4R))= (q^(2))/( 16 pi epsilon_(0)R)`
(ii) Potential energy of the system `= ( 1)/( 4 pi epsilon_(0) ) ( q(-q))/( 2R)= ( -1 )/( 4pi epsilon_(0)) (q^(2))/( (2R)) = ( - q^(2))/( 8 pi epsilon_(0)R)`
(iv) Total energy of the system = K.E. `+` P.E. `= ( -q^(2))/( 4pi epsilon_(0)(4R))= ( -q^(2))/( 16 pi epsilon_(0)R)`
Note `:` K.E. `| (1)/(2) P.E.|,T.E. = ( P.E.)/(2)`