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A parallel plate capacitor made of circular plates each of radius R 6 …

A parallel plate capacitor (Fig. 8.7) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s^–1.
(a) What is the rms value of the conduction current?
(b) Is the conduction current equal to the displacement current?
(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

A parallel plate capacitor made of circular plates each of radius R 6

Ans: Given: R = 6.00 cm, C = 100 pF = 10^-10 F, V_rms = 230V, Angular frequency (omega) = 300 rad s^–1

(a) I_rms =?

I_rms = V_rms / Xc = V_rms omega C

$I_rms = 230 * 300 * {10^-10} = 6.9 * 10^-6 A$

(b) Is the conduction current equal to the displacement current?

Yes, conduction current is equal to the displacement current even if current is varying.

(c) B₀ = ? at a point r = 3.0 cm from the axis between the plates.

Magnetic field due to circular disc at a point its axis $B_0 = {mu_0 r I_0} / {2 pi R^2} = {mu_0 r (I_rms sqrt{2})} / {2 pi R^2}$

r- distance of observation point from centre of disc
R- radius of disc

$B_0 = {(2 * 10^-7 ) * (3 * 10^-2) * (6.9 * 10^-6 * 1.41)} / (6 * 10^-2)^2 = 1.63 * 10^-11 T$

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A parallel plate capacitor made of circular plates each of radius R 6, A parallel plate capacitor made of circular plates each of radius R 6

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