Two identical charged conducting spheres A and B have their centres separated by a certain distance. The charge on each sphere is q and the force of repulsion between them is F. A third identical unch

Question

Two identical charged conducting spheres A and B have their centres separated by a certain distance. The charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B, and finally removed from both. The new force of repulsion between spheres A and B (the radii of A and B are negligible compared to the distance of separation, so they can be considered point charges) is best given as:

Vishal Gupta · Accepted Answer

D. Touching A: the third sphere and A share q, so A becomes q/2. Touching B: it carries q/2 to B, which then holds \frac{q/2 + q}{2} = \frac{3q}{4}. New force \propto \frac{q}{2}\cdot\frac{3q}{4} = \frac{3}{8}q^2, i.e. \frac{3F}{8}.

Electric Charges and Fields

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