Walker, Halliday & Resnick — Maxwell's Equations; Magnetism of Matter: Problem 49

49 In Fig. 32-30, a capacitor with circular plates of radius $R = 18.0 \text{ cm}$ is connected to a source of emf $\mathcal{E} = \mathcal{E}_m \sin \omega t$, where $\mathcal{E}_m = 220 \text{ V}$ and $\omega = 130 \text{ rad/s}$. The maximum value of the displacement current is $i_d = 3.80 \text{ }\mu\text{A}$. Neglect fringing of the electric field at the edges of the plates. (a) What is the maximum value of the current $i$ in the circuit? (b) What is the maximum value of $d\Phi_E/dt$, where $\Phi_E$ is the electric flux through the region between the plates? (c) What is the separation $d$ between the plates? (d) Find the maximum value of the magnitude of $B$ between the plates at a distance $r = 11.0 \text{ cm}$ from the center.