All Problems

Electric Current

Problem 3.203

The radii of spherical capacitor electrodes are equal to \(a\) and \(b,\) with \(a< b .\) The interelectrode space is filled with homogeneous substance of permittivity \(\varepsilon\) and resistivity \(\rho .\) Initially the capacitor is not charged. At the moment \(t=0\) the internal electrode gets a charge \(q_{0}\). Find: (a) the time variation of the charge on the internal electrode; (b) the amount of heat generated during the spreading of the charge.

Reveal Answer
 (a) q=q0et/ε0ερ; (b) Q=(1/a1/b)q02/8πε0ε\text { (a) } q=q_{0} \mathrm{e}^{-t / \varepsilon_{0} \varepsilon \rho} ; \text { (b) } Q=(1 / a-1 / b) q_{0}^{2} / 8 \pi \varepsilon_{0} \varepsilon