Suppose that a parallel-plate capacitor has circular plates with radius R and a

Question

Suppose that a parallel-plate capacitor has circular plates with radius R and a plate separation d. Suppose also that a sinusoidal potential difference with a maximum value Vm and an angular frequency ? is applied across the plates; that is,

V = Vm sin ?t

Chapter 32, Problem 7 SN 3 Incorrect Suppose that a parallel-plate capacitor has circular plates with radius R and a plate separation d. Suppose also that a sinusoidal potential difference with a maximum value Vm and an angular frequency w is applied across the plates; that is, Find B max(R), the maximum value of the induced magnetic field that occurs at r-R, in terms of the given variables. UseEO and if needed. Click here to enter or edit your answer cos(t Bmax(R) = cos t 0 *0 m2 d Click if you would like to Show Work for this question: Open Show Work

Explanation / Answer

here

the B field can be calculated from the rate of change of electric flux using

integrate( B. dl) = u0 * i

i = is the displacement currrent

i = e0 * df/dt

f is the electric flux

we are given the voltage V from which the electric field E = V / d

d is the plate seperation

the rate of change of electric flux is = dE/dt = Vm * w * cos(w * t) / d

when r = R , the integral is = integrate( B . dl) = B * 2 * pie * R

thus the maximum B field is Bmax = u0 * e0 * Vm * w * pie * R^2 / d / 2*pie*R

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