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. $\sqrt{\frac{16 \pi^{3} \varepsilon_{0} m r^{3}}{q_{1} q_{2}}}$
• B. $\sqrt{\frac{8 \pi^{3} \varepsilon_{0} m r^{3}}{q_{1} q_{2}}}$
• C. $\sqrt{\frac{q_{1} q_{2}}{16 \pi^{3} \varepsilon_{0} m r^{3}}}$
• D. Zero

Answer 1

Answer: (A)

$\frac{m v^{2}}{r}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} \,q_{2}}{r^{2}}$
$v=\left[\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r m}\right]^{\frac{1}{2}}$
For $1$ trip
$T=\frac{2 \pi r}{v}=2 \pi r\left[4 \,\pi\, \varepsilon_{0} m r\right]\left[q_{1} \,q_{2}\right]^{\frac{1}{2}} $
$T=\sqrt{\frac{16 \pi^{3}\, \varepsilon_{0} \,m r^{3}}{q_{1}\, q_{2}}}$