Question

Find the capacitance of a spherical capacitor whose electrodes have radii R₁ and R₂ > R₁ and which is filled with isotropic dielectric whose permittivity varies as ε = a/r, where a is a constant, and r is the distance from the centre of the capacitor.

Answer 1

Let, us mentally impart a charge q to the conductor. Now potential difference between the plates, 

Hence, the sought capacitance,