The capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere. The ratio of their radii is

Assuming ab expression for the potential of an isolated conductor, show that the capacitance of such a sphere will be increased by a factor n, if it is enclosed within an earthed concentric sphere, the ration of the spheres being n(n - 1) .

The capacitance (C ) for an isolated conducting sphere of radius (a) is given by 4pi epsilon_(0)a . If the sphere is enclosed with an earthed concentric sphere. The ratio of the radii of the sphere being (n)/((n-1)) then the capacitance of such a sphere will be increased by a factor

A sphere and a hemisphere have the same volume. The ratio of their radii is

The capacitance of an isolated conducting sphere of radius R is proportional to

If the radius of a sphere is increased to three times its previous value, the volume of the sphere increases to :