Question 33 of 311

A certain charge $Q$ is divided into two parts $q$ and $(Q-q).$ How should the charges $Q$ and $q$ be divided so that $q$ and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?

A$Q=\dfrac{q}{2}$B$Q=2q$C$Q=4q$D$Q=3q$

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Answer: (B) $Q=2q$

${F}_{q}=\dfrac{kq(Q-q)}{{L}^{2}}=\dfrac{k}{{L}^{2}}\left(qQ-{q}^{2}\right)$
$\dfrac{\text{d}F}{\text{d}q}=0$ when force is maximum
$\dfrac{\text{d}F}{\text{d}q}=\dfrac{k}{{L}^{2}}[Q-2q]=0$
$\Rightarrow Q-2q=0\Rightarrow Q=2q$