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. $\frac{C}{12}$
• B. $12C$
• C. $144C$
• D. Only Batman knows because he’s Batman!

Answer 1

The correct option is B $12C$

The capacitance of a spherical conductor is given by $4\pi {\epsilon }_{0}R$ , 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 $\frac{KQ}{R}.AsC=\frac{Q}{V}$, on dividing Q by $\frac{KQ}{R}weget4\pi {\epsilon }_{0}R]$ 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