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A parallel plate capacitor made of circu...

A parallel plate capacitor made of circular plates each of radius `R= 6.0` cm has a capacitance `c = 100pF`. The capacitor is connected to a `230 V AC` supply with a ( angular) frequency of `300 rad//s`
(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.
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Text Solution

Verified by Experts

(a) `I_("rms") =V_("rms") omega C=6.9 mu A`
(b) Yes. The derivation in Exercise 8.1(b) is true even if i is oscillating in time.
(c ) The formula `B =(mu_(0) r)/(2 pi R^(2)) i_(d)`
goes through even if `i_(d)` (and therefore B) oscillates in time. The formula shows they oscillate in phase. Since `i_(d)= i`, we have
`B_(0)=(mu_(0) r)/(2 pi R^(2)) i_(0)`," where "B_(0) and i_(0)` are the amplitudes of the oscillating magnetic field and current, respectively. `i_(0) =sqrt(2) I_("rms")=9.76 mu A.` For `r=3 cm, R=6 cm, B_(0)=1.63xx10^(-11) T.`
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