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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 σ\sigma and permittivity ε.\varepsilon . The capacitor plates shaped as round discs are separated by a distance dd. Neglecting the edge effects, find the magnetic field strength between the plates at a distance rr from their axis if an ac voltage V=Vmcos⁡ωtV=V_{m} \cos \omega t is applied to the capacitor

Reveal Answer
 3.350. H=Hmcos⁡(ωt+α), where Hm=rVm2dσ2+(ε0εω)2 \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 α\alpha is determined from the formula tan α=ε0εω/σ\alpha=\varepsilon_{0} \varepsilon \omega / \sigma.
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