Question

A charge $q$ is to be distributed on two conducting spheres. What should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in air?

• A. $\frac{q}{2}$ and $\frac{q}{2}$
• B. $\frac{q}{4}$ and $\frac{3 q}{4}$
• C. $\frac{q}{3}$ and $\frac{2 q}{3}$
• D. $\frac{q}{5}$ and $\frac{4 q}{5}$

Answer 1

Answer: (A)

Force between both is
$F=\frac{K Q(q-Q)}{r^{2}}$
If $F=$ maximum then
$\frac{d F}{d Q}=0$
So $Q=\frac{q}{2}$
So both charge be $\frac{q}{2}, \frac{q}{2}$