# Charges wants freedom!

**Electricity and Magnetism**Level 3

Two small equally charged spheres each of mass m are suspended from the same point by silk thread of length \(l\) the distance between the spheres initially is \(x\) which is very small as compared to \(l\). Some how the charge on the spheres starts leaking out. Find the rate \(\frac{dq}{dt}\) with which the charge leaks off each spheres; if their approach velocity varies as \(v=\frac{C}{\sqrt{x}}\); where \(C\) is a constant.

if the answer can be represented in this form: \[\frac{dq}{dt}=\frac{a}{b}C\sqrt{\frac{fmg\pi\epsilon_{0}}{l}}\]

then find the value of \(a+b+f\)?