Question

A particle of mass m and carrying charge -q1 is moving around acharge +q2 along a circular path of radius r .Prove that the period of revolution of the charge -q1 about +q2 is given by

Answer 1

A particle of mass m and carrying a charge $-q_1$ moving around a charge $+q_2$ along circular path of radius r.

we know, positive charge attracts negative charge. here moving charge $-q_1$ is attracted by charge $+q_2$ placed at centre of circular path of radius r but this force is balanced by centripetal force.

so, centripetal force = electrostatic force between them,

or, $m\omega^2 r=\frac{kq_1q_2}{r^2}$

or, $\omega^2=\frac{kq_1q_2}{mr^3}$

or, $\omega=\sqrt{\frac{kq_1q_2}{mr^3}}$

we know, angular frequency = 2π/time period

so, Time period , T = $2\pi\sqrt{\frac{mr^3}{kq_1q_2}}$

Answer 2

I hope it is helpful for u