A certain charge Q is divided into two parts q and (Q-q) . How should charges Q and q be divided so

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1. Electric Charges and Fields

medium

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

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

B

${Q}=3 {q}$

C

$Q=2 q$

D

$Q=4 q$

(JEE MAIN-2021)

Solution

$F=\frac{k Q(Q-q)}{\pi^{2}}$

$\frac{d F}{d q}=0$ When force is maximum

$\frac{d F}{d q}=\frac{k}{L^{2}}[Q-2 q]=0$

$\Rightarrow Q-2 q=0 \Rightarrow Q=2 q$

Standard 12

Physics

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