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A charge ‘Q’ is to be divided into two small parts. What should be the value of the charges on the parts so that the force between the parts will be maximum ?

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$q_{1} = \frac{Q}{4}, q_{2} = \frac{3 Q}{4}$

$q_{1} = \frac{Q}{2}, q_{2} = \frac{Q}{2}$

$q_{1} = \frac{Q}{3}, q_{2} = \frac{2 Q}{3}$

$q_{1} = \frac{Q}{2}, q_{2} = \frac{3 Q}{2}$

answer is B.

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Detailed Solution

$F = \frac{1}{4 π \in_{0}} \frac{(Q - q) q}{r^{2}}$

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

$\frac{d}{d q} (Q - q) q = 0 \Rightarrow (Q - a) + (- q) = 0$

$\Rightarrow Q - 2 q = 0 i . e q = \frac{Q}{2}$

Thus the charge should be divided equally on the object

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