Question #43253

A parallel plate capacitor with circular plates of radius $R = 5 \text{ cm}$ is filled with a lossy dielectric material. The material has a relative permittivity (dielectric constant) $K = 9$ and a uniform electrical conductivity $\sigma = \sqrt{3} \times 10^{-3} \text{ S/m}$. An alternating electric field $E(t) = E_0 \sin(\omega t)$ is established inside the dielectric, where $E_0 = 5 \times 10^4 \text{ V/m}$ and $\omega = 4\pi \times 10^6 \text{ rad/s}$. Neglecting edge effects, what is the amplitude of the induced magnetic field $B_{max}$ at a radial distance $r = 2 \text{ cm}$ from the central axis of the capacitor? (Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2$ and $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)