Question

Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x << l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v = a/\(\sqrt V\) bar x, where a is a constant.

Answer 1

Let the balls be deviated by an angle θ, from the vertical when separtion between them equals x.

Applying Newton’s second law of motion for any one of the sphere, we get, 

T cos θ = mg    .....(1)

and T sin θ = F     ......(2) 

From the Eqs. (1) and (2)