Question

Two small equally charged spheres, each of mass mm, are suspended from the same point by silk threads of length l. The distance between the spheres x << l. Find the rate $\frac{dq}{dt}$ with which the charge leaks off each sphere if their approach velocity varies as $v=\frac{a}{\sqrt{x}}$, where a is a constant $(k=\frac{1}{4\pi {\epsilon }_0})$.

• A. $\frac{3a}{2}\sqrt{\frac{mg}{2kl}}$
• B. $\frac{a}{2}\sqrt{\frac{mg}{2kl}}$
• C. $\sqrt{\frac{mg{a}^2}{2kl}}$
• D. $\sqrt{\frac{3mga}{2kl}}$

Answer 1

The correct option is A $\frac{3a}{2}\sqrt{\frac{mg}{2kl}}$