Question
A and B are two conducting spheres of equal radius, in which sphere $A$ is solid and sphere $B$ is hollow. Both are charged to the same potential. What will be the relation between the charges on both the spheres?
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Answer
Whether the sphere is solid or hollow, the charge remains on its outer surface. Since the capacitance of a spherical conductor is directly proportional to its radius. Here both the spheres have the same radius. Therefore, the capacitance of both will also be equal. Therefore, $C _{ A }= C _{ B }=$ C , meaning both the spheres are charged with the same potential (say up to V ). That is, $V _{ A }= V _{ B }= V$, therefore their charges are $Q _{ A }= C _{ A } V _{ A }= CV , Q _{ B }= C _{ B } V _{ B }= CV$ respectively.
Therefore $Q _{ A }: Q _{ B }=1: 1$ i.e. charge on both will be equal.
Therefore $Q _{ A }: Q _{ B }=1: 1$ i.e. charge on both will be equal.
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