Two equally charged identical metal spheres A and B repel each other with a force F. Another identical uncharged sphere C is touched to A and then placed midway between A and B. The net force on C is in the direction

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F towards B

2F towards B

2F towards A

F towards A

answer is A.

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Detailed Solution

$F = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{r^{2}}$

When the uncharged sphere touches A, q/2 charge gets transferred to C
Now, force on C,

$= \frac{k (q / 2) (q / 2)}{(r / 2)^{2}} - \frac{k (q / 2) (q)}{(r / 2)^{2}} = {kq}^{2} / r^{2} - 2 kq {}^{2}/ r^{2} = - F$

Net force is thus towards A.

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