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?

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) (q/2) and (q/2) (B) (q/4) and (3 q/4) (C) (q/3) and (2 q/3) (D) (q/5) and (4 q/5)

Tardigrade Admin · Accepted Answer

Force between both is F=(K Q(q-Q)/r2) If F= maximum then (d F/d Q)=0 So Q=(q/2) So both charge be (q/2), (q/2)

Q. 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?

$\frac{q}{2}$ and $\frac{q}{2}$

$\frac{q}{4}$ and $\frac{3 q}{4}$

$\frac{q}{3}$ and $\frac{2 q}{3}$

$\frac{q}{5}$ and $\frac{4 q}{5}$

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 $\frac{q}{2}, \frac{q}{2}$

Q. 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?

2q​ and 2q​

4q​ and 43q​

3q​ and 32q​

5q​ and 54q​