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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 :

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

$F=\large\frac{1}{4 \pi \in _0} \frac{q (Q-q)}{r^2}$
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.