Question

Charge $q_2$ of mass m revolves around a stationary charge $q_1$ in a circular orbit of radius r. The orbital periodic time of $ q_2 $ would be

• A. $ \bigg [ \frac{ 4 \pi^2 \, mr^3 }{ kq_1 \, q_2 } \bigg]^{ 1/2}$
• B. $ \bigg [ \frac{ kq_1 \, q_2 }{ 4 \pi^2 \, mr^3 } \bigg]^{ 1/2}$
• C. $ \bigg [ \frac{ 4 \pi^2 \, mr^4 }{ kq_1 \, q_2 } \bigg]^{ 1/2}$
• D. $ \bigg [ \frac{ 4 \pi^2 \, mr^2 }{ kq_1 \, q_2 } \bigg]^{ 1/2}$

Answer 1

Answer: (A)

$ \frac{ 1}{ 4 \pi \varepsilon_0} \frac{ q_1 \, q_2 }{ r^2 } = mr \omega^2 = \frac{ 4 \pi^2 mr }{ T^2} $
$ T^2 = \frac{ ( 4 \pi \varepsilon_0 ) r^2 \, ( 4 \pi^2 \, mr )}{ q_1 \, q_2 } $
$ \bigg [ \frac{ 4 \pi^2 \, mr^3 }{ kq_1 \, q_2 } \bigg]^{ 1/2}$