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Two point charges $3 \times 10^{-6} \,C$ and $8 \times 10^{-6} \, C$ repel each other by a force of $6 \times 10^{-3} \, N$. If each of them is given an additional charge $-6 \times 10^{-6} \, C$, the force between them will be
$2.4 \times 10^{-3} $ $N$ (attractive)
$2.4 \times 10^{-9} $ $N$ (attractive)
$1.5 \times 10^{-3} $ $N$ (repulsive)
$1.5 \times 10^{-3}$ $N$ (attractive)
Solution
(d)$F \propto {Q_1}{Q_2}$ $==>$ $\frac{{{F_1}}}{{{F_2}}} = \frac{{{Q_1}{Q_2}}}{{{Q_1}'{Q_2}'}}$
$ = \frac{{3 \times {{10}^{ – 6}} \times 8 \times {{10}^{ – 6}}}}{{(3 \times {{10}^{ – 6}} – 6 \times {{10}^{ – 6}})(8 \times {{10}^{ – 6}} – 6 \times {{10}^{ – 6}})}} = \frac{{3 \times 8}}{{ – \,3 \times 2}} = – \frac{4}{1}$
$==>$ ${F_2} = – \frac{{{F_1}}}{4} = – \frac{{6 \times {{10}^{ – 3}}}}{4} = – 1.5 \times {10^{ – 3}}\,N$ (Attractive)