A certain charge Q is divided into two parts q and (Q-q). How should the charges Q and q be divided so that q and (Q-q) placed at a certain distance apart experience maximum electrostatic repulsion?

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Q=q/2

Q =2q

Q = 4q

Q = 3q

answer is B.

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Detailed Solution

Let two parts of charge Q be divided into q and Q – q
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$F = \frac{{Kq}_{1} q_{2}}{r^{2}} = \frac{K (q) (Q - q)}{r^{2}}$
For maximum repulsion $\frac{dF}{dq} = 0 or \frac{d}{dq} [\frac{Kq (Q - q)}{r^{2}}] = 0 \Rightarrow Q - 2 q = 0 \Rightarrow Q = 2 q$

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