All Problems

Electric Capacitance, Energy of an Electric Field

Problem 3.105

Find the capacitance of a spherical capacitor whose electrodes have radii \(R_{1}\) and \(R_{2}>R_{1}\) and which is filled with isotropic dielectric whose permittivity varies as \(\varepsilon=a / r,\) where \(a\) is a constant, and \(r\) 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)