• question_answer The conducting spheres of radii r and 3r initially have charges 3q & q respectively. Their separation is much larger than their radii. If they are joined by a conductor of high resistance, the force between them will - A) Increase continuously B) Decrease continuously C) First increase, then decrease D) First decrease, then increase

 Let charge on smaller sphere be x and on larger sphere be $4q-x$ Force between them is given by $F=\frac{kx\,\,(4q-x)}{{{d}^{2}}}$ $\frac{dF}{dx}=0\Rightarrow 4q-2x=0\Rightarrow x=2q$
 $\frac{{{d}^{2}}F}{d{{x}^{2}}}=\frac{K}{{{d}^{2}}}(-\,2)<0$ $\therefore$It represents a maximum. Final charges on the smaller sphere and the larger sphere are q & 3q respectively as required by the equality of potentials $\therefore$Force will increase until the charges becomes equal and after that force will decreases.