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

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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