Question

A charge $Q$ is to be distributed on two objects, $A$ and $B.$ The values of the charges on the objects are such that the force between the objects will be maximum. The ratio $Q_A:Q_B$ will be

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

The correct option is B $1:2$

Let the charge distribution on the two objects be $q$ and $Q-q$

The force acting between them is

$F=\frac{q\left(Q-q\right)}{R^2}$

Since the force acting between them is given maximum.

$\frac{dF}{dq}=0$

$F=\frac{qQ-q^2}{R^2}$

On differentiating and solving we get

$\frac{dF}{dq}=\frac{Q-2q}{R^2}=0$

$Q=2q$

Hence the ration is $1:2$