All Problems Electromagnetic Induction. Maxwells Equations
Problem 3.350
The space between the electrodes of a parallel-plate capacitor is filled with a uniform poorly conducting medium of conductivity \(\sigma\) and permittivity \(\varepsilon .\) The capacitor plates shaped as round discs are separated by a distance \(d\). Neglecting the edge effects, find the magnetic field strength between the plates at a distance \(r\) from their axis if an ac voltage \(V=V_{m} \cos \omega t\) is applied to the capacitor
\[ \text { 3.350. } H=H_{m} \cos (\omega t+\alpha), \quad \text { where } \quad H_{m}=\frac{r V_{m}}{2 d} \sqrt{\sigma^{2}+\left(\varepsilon_{0} \varepsilon \omega\right)^{2}} \] and \(\alpha\) is determined from the formula tan \(\alpha=\varepsilon_{0} \varepsilon \omega / \sigma\).