All Problems

Electric Capacitance, Energy of an Electric Field

Problem 3.105

Find the capacitance of a spherical capacitor whose electrodes have radii R1R_{1} and R2>R1R_{2}>R_{1} and which is filled with isotropic dielectric whose permittivity varies as ε=a/r,\varepsilon=a / r, where aa is a constant, and rr is the distance from the centre of the capacitor.

Reveal Answer
C=4πε0a/ln(R2/R1)C=4 \pi \varepsilon_{0} a / \ln \left(R_{2} / R_{1}\right)