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

The correct option is A $\sqrt{\frac{16{\pi }^3{\epsilon }_{0}m{r}^3}{q_1{q}_2}}$

Magnitude of attraction force should be equal to centripetal force ,$mr{\omega }^2$

so we get $\left(q_1{q}_2/4\pi {ϵ}_0{r}^2\right)=mr{\omega }^2$

From here we will get value of $\omega$ and by putting value of $\omega$ in $T=2\pi /\omega$

we get time period $T=\sqrt[2]{216{\pi }^{3}m{r}^3{ϵ}_0/\left(q_1{q}_2\right)}$.

option A is correct.