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A change A is divided into two parts: q and Q-q. if Coulomb repulsion between them when they are separated is maximum , $\large\frac{Q}{Q-q}$ should be :

$(A)\;1 \\ (B)\;2 \\ (C)\; \frac{1}{2} \\ (D)\;\frac{1}{4} $

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$F=\large\frac{1}{4 \pi \in _0} \frac{q (Q-q)}{r^2}$
r is constant
$\therefore$ for F to be maximum
$\large\frac{dF}{dq} $$=0$
=> $\large\frac{1}{4 \pi \in _0 r^2}\frac{d(q(Q-q))}{dq}=0$
=> $Q-2q=0$
=> $Q= 2q$
=> $q= \large\frac{Q}{2}$
So, $\large\frac{Q}{Q-q}$$=2$
Hence B is the correct answer.
answered Jan 3, 2014 by meena.p

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