Spherical Capacitor

Let us consider a charged metallic sphere of radius r, placed in the air or any other dielectric medium without touching the earth. We may also consider that, the sphere is charged with Q coulomb, and the relative permittivity of air or medium in which the sphere is placed is εr.
Now as per definition, the surface potential of this sphere will be

Since, as per definition, capacitance C = Q/V
So, it is proved that the capacitance of a conducting sphere is directly proportional to it’s radium and also to the permittivity of the medium in which the sphere is placed.

Now, let us consider two concentric spheres of radius r1 and r2 respectively. The inner sphere is connected with positive terminal of a battery and outer sphere is connected with negative terminal of the battery. For that there will be Q charge is accumulated in the system.
Now, according to the definition, the surface potential of inner sphere is

And surface potential of other sphere is

Now, the potential difference between there are two spheres is,

Again as per definition,

This is nothing but the capacitance of a hollow spherical capacitor whose thickness is

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