Question

A charge $Q$ is to be divided into two parts : $q$ and $Q - q$. What is the relation between $q$ and $Q$ if the two parts, when placed apart, has maximum coloumb repulsion

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

Answer 1

Answer: (D)

$q = \frac{Q}{2}$

Answer 2

Charge $Q$ is divided into two parts $q$ and $Q - q$ and let they are placed d distance apart where the coloumb repulsion is maximum.
$\therefore \:\:\: \frac{dF_e}{dq} = \frac{d}{dq} \left[ \frac{Kq (Q - q) }{d^2} \right] = 0$
or $\frac{K}{d^2} \frac{d}{dq} (qQ - q^2) = 0$ or $Q = 2q$
$\therefore \:\:\: q = \frac{Q}{2}$