a charge q is to be distributed on two conducting spheres. what should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in air?
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When a charge of equal magnitude is placed on both the conducting spheres, then only the repulsive force between them shall be maximum. ... Therefore, since the distance is fixed, equal charges will have maximum product therefore the charge q be equally distributed as q / 2 on each of conducting sphere.
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Suppose, one object receives a charge say q and the other Q - q . Thus, the force between the objects is
F = kq (Q−q) / d²
For F to be max dF/dq = 0
Q−2q = 0
q = Q/2
Therefore, since the distance is fixed, equal charges will have maximum product therefore the charge q be equally distributed as q / 2 on each of conducting sphere.
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