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Question

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is F. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and the removed. As a result, the force between A and B would be equal to

A
3F4
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B
F2
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C
F
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D
3F8
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Solution

The correct option is D 3F8
Initially charges on both sphere, q

F=Kq2d2 .............(1)

When sphere C will get touched with sphere A, then final charges on both will become q2.

Now, when this sphere C will get touched to sphere B, then final charges on both of them will be
qc=qd=q/2+q2=3q4

Now force between A and B will be
F=k×q2×3q4d2
F=3F8

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