Q: A particle of mass ‘m’ carrying a charge –q_{1} is moving around a fixed charge +q_{2} along a circular path of radius ‘ r ’ find time period of revolution of charge q_{1} .

Sol. Electrostatic force on -q_{1} to +q_{2} will provide the necessary centripetal force

$\large \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r^2} = \frac{m v^2}{r} $

$\large v = \sqrt{\frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{ m r}}$

Time Period $\large T = \frac{2 \pi r}{v}$