The capacitance of a spherical conducting capacitor is C. It is placed inside an earthed sphere in such a way that their centers are at the same point. Prove that the capacitance of the spherical charged capacitor will be n times the initial capacitance C, if the ratio of their radius is n:(n-1).

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A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.

(a) Determine the capacitance of the capacitor.

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