Walker, Halliday & Resnick — Maxwell's Equations; Magnetism of Matter: Problem 47

47 Suppose that a parallel-plate capacitor has circular plates with radius \(R = 30 \text{ mm}\) and a plate separation of \(7.5 \text{ mm}\). Suppose also that a sinusoidal potential difference with a maximum value of \(150 \text{ V}\) and a frequency of \(60 \text{ Hz}\) is applied across the plates; that is, \[V = (150 \text{ V}) \sin[2\pi(60 \text{ Hz})t].\] (a) Find \(B_{\text{max}}(R)\), the maximum value of the induced magnetic field that occurs at \(r = R\). (b) Plot \(B_{\text{max}}(r)\) for \(0 < r < 10 \text{ cm}\).