Question

The time period of revolution of a charge \(q_1\) and of mass \(m\) moving in a circular path of radius \(r\) due to Coulomb force of attraction with another charge \(q_2\) at its centre is

• A. \(\sqrt{\frac{16\pi^3 \epsilon_0 mr^3}{q_1 q_2}}\)
• B. \(\sqrt{\frac{8\pi^2 \epsilon_0 mr^3}{q_1 q_2}}\)
• C. \(\sqrt{\frac{\epsilon_0 mr^3}{16\pi q_1 q_2}}\)
• D. \(\sqrt{\frac{16\pi^3 \epsilon_0 mr^3}{q_1 q_2}}\)
• E. \(\sqrt{\frac{\pi^2 \epsilon_0 mr^3}{8q_1 q_2}}\)

Hint:

This derivation is identical to Kepler's Third Law for planets, where \(T^2 \propto r^3\). The constant of proportionality here simply uses electrical units instead of gravitational ones!

Answer 1

The Correct Option is D