Question

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

• A. $\sqrt{\frac{16{\pi }^3{\epsilon }_{0}m{r}^3}{q_1{q}_2}}$
• B. $\sqrt{\frac{8{\pi }^3{\epsilon }_{0}m{r}^3}{q_1{q}_2}}$
• C. $\sqrt{\frac{q_1{q}_2}{16{\pi }^3{\epsilon }_{0}m{r}^3}}$
• D. Zero

Answer 1

Answer: (A)

$\frac{m{v}^2}{r}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_1{q}_2}{r^2}$
$v={\left[\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{rm}\right]}^{\frac{1}{2}}$
For $1$ trip
$T=\frac{2\pi r}{v}=2\pi r\left[4\pi {\epsilon }_{0}mr\right]{\left[q_1{q}_2\right]}^{\frac{1}{2}}$
$T=\sqrt{\frac{16{\pi }^3{\epsilon }_{0}m{r}^3}{q_1{q}_2}}$