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  4. A charge Q is divided into two parts of q and Q-q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of (Q/q) should be

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Q. A charge $Q$ is divided into two parts of $q$ and $Q-q$. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

AIIMSAIIMS 2011

Solution:

Let distance between two charges is $x$
The force between them.
$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q(Q-q)}{x^{2}}$
$x$ is constant, so for maximum force $q(Q-q)$ should be maximum.
$\frac{ d }{ L q}\{q(Q-q)\}=0$
$Q-2 q=0$
$\Rightarrow \frac{Q}{q} =2$