Exercise 29.42 A parallel-plate air-filled capacitor is being charged as in the

Question

Exercise 29.42

A parallel-plate air-filled capacitor is being charged as in the figure (Figure 1) . The circular plates have radius 4.04cm , and at a particular instant, the conduction current in the wires is 0.286A .

Part A

What is the displacement current density jD in the air space between the plates?

jD = A/m2  

Part B

What is the rate at which the electric field between the plates is changing?

dEdt = V/m?s  

Part C

What is the induced magnetic field between the plates at a distance of 1.93cm from the axis?

B1 = T

Part D

What is the induced magnetic field between the plates at a distance of 1.10cm from the axis?

Explanation / Answer

a) The displacement current density = i2 / pi r2

= 0.286 / (pi * (4.04 * 10-2)2)

= 55.78 A/m2

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b)  rate at which the electric field between the plates is changing = J / E0

= 55.78 / (8.85 * 10-12)

= 6.30 * 1012 V/m.s

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c) B = [mu / 2 pi][r/R2][i]

= 2 * 10-7 * 1.93 * 10-2 * 0.286 / ((4.04 * 10-2)2)

= 6.76 * 10-7 T

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d) B = [mu / 2 pi][r/R2][i]

= 2 * 10-7 * 1.10 * 10-2 * 0.286 / ((4.04 * 10-2)2)

= 3.86 * 10-7 T

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