A charg Q is divided into two parts q and Q-q and separated by a distance R . force of repulsion bet

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1. Electric Charges and Fields

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A charg $Q$ is divided into two parts $q$ and $Q-q$ and separated by a distance $R$ . The force of repulsion between them will be maximum when

A

$q = Q/4$

B

$q = Q/2$

C

$q = Q$

D

none of these

Solution

$F=\frac{k q(Q-q)}{r^{2}}\left(\text { where } k=\frac{1}{4 \pi \varepsilon_{0}}\right)$

For $F$ to be maximum $\frac{d F}{d q}=0$

By putting $\frac{d F}{d q}=0$ we get

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

Standard 12

Physics

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