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Question

The radius of Krypton, the home planet of the famous D.C comic super-hero Superman, is 12 times the radius of earth. If the capacitance of earth is C, what will be the capacitance of Krypton?

A
C12
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B
12C
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C
144C
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D
Only Batman knows because he’s Batman!
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Solution

The correct option is B 12C
The capacitance of a spherical conductor is given by 4πε0 R , where R is the radius of the spherical conductor. [If you don’t buy that then recall that if a Q charge was placed on a spherical conductor its potential on the surface would become KQR.As C=QV, on dividing Q by KQR we get 4πε0 R] As the radius is 12 times that of earth and capacitance is directly proportional to radius, the capacitance of Krypton would be 12C. If you focus, you too can be Batman :P

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