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Two identical small metal spheres A and B carry charges +4q and −4q, respectively. If they are kept at a fixed separation, the electrostatic force between them is F. Now a third identical sphere C, initially neutral, is first brought into contact with A, then with B, and finally taken away to infinity. For the same separation between A and B, what will be the new force of interaction between them?

1. F/2
2. F/8
3. F/16
4. F/32

Correct answer: F/8

Solution

When sphere C, initially neutral, comes into contact with sphere A, it acquires a charge of +2q, and when it contacts sphere B, it acquires a charge of -2q. After these interactions, sphere A has a charge of +2q and sphere B has a charge of -2q, resulting in a new electrostatic force that is one-fourth of the original force F, leading to a final interaction force of F/8.

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