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Question

A charge 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
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B
q=Q/2
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C
q=Q
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D
none of the above
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Solution

The correct option is A $$\displaystyle q = Q/2$$

We have force of repulsion between the two charges,

$$ F_r = \dfrac {1}{4 \pi \varepsilon_0} \dfrac {q (Q - q)}{ R^2}$$

Now

(a)if $$ q = \dfrac {Q}{4}$$, force $$F = \dfrac{1}{4 \pi \varepsilon_0} \dfrac {3Q}{16}$$

(b)if $$q = \dfrac {Q}{2}$$, force $$F = \dfrac {1}{4 \pi \varepsilon_0} \dfrac {Q}{4}$$

(c) if $$ q = Q$$,  force $$F = 0$$

Hence the force of repulsion between them will be maximum when $$q = \dfrac {Q}{2}$$.


Physics

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