Question

A charge $Q$ is to be divided into two parts, $q$ and $(Q- q)$, such that force between them is maximum. Then

• A. $Q = 3q$
• B. $Q = 1.5 q$
• C. $Q = 2q$
• D. $Q = 4 q$

Answer 1

Answer: (C)

$Q = 2q$

Answer 2

$F =k \frac{q\left(Q - q\right)}{r^{2}}$
$\frac{dF}{dq} = \frac{k}{r^{2}} \left[\left(Q -q\right) + q\left(-1\right)\right]$
$\, \, \, \, = \frac{k}{r^{2}} \left(Q -2q\right)$
For maximum value of $F, \frac{dF}{dq} = 0$
$\therefore \, \frac{k}{r^{2} } \left(Q - 2q\right)= 0$
or, $Q = 2q$