A charge having magnitude ‘Q’ is divided into two parts q and (Q - q) which are held a certain distance ‘r’ apart. The force of repulsion between the two parts will be maximum if the ratio q/Q is

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A charge having magnitude ‘Q’ is divided into two parts q and (Q - q) which are held a certain distance ‘r’ apart. The force of repulsion between the two parts will be maximum if the ratio q/Q is

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$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

answer is A.

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Detailed Solution

The force of repulsion between the two parts is given by

$F = \frac{1}{4 {πε}_{0}} \frac{q (Q - q)}{r^{2}} F o r t o b e m a x i m u m, \frac{d F}{d q} = 0, \frac{d}{d q} [\frac{1}{4 {πε}_{0}} \frac{q (Q - q)}{r^{2}}] = 0 S i n c e r i s f i x e d, w e h a v e \frac{d}{d q} [q (Q - q)] = 0 \Rightarrow Q - 2 q = 0 \frac{q}{Q} = \frac{1}{2}$