Question

A charge Q is to be divided into two parts q and (Q-q) such that the force between them is maximum at a certain distance. The value of q is

• A. $\frac{Q}{3}$
• B. $\frac{Q}{2}$
• C. $\frac{Q}{4}$
• D. $\frac{3Q}{4}$

Answer 1

The correct option is B $\frac{Q}{2}$

$F=K\frac{q(Q-q)}{x^2}=\frac{k[qQ-q^2]}{x^2}$
$\frac{dF}{dp}=\frac{k}{x^2}[Q-2q]$
For maximum force $\frac{dF}{dq}=0$
0 = Q - 2q
Q = 2q
$Q=\frac{Q}{2}$