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A parallel plate capacitor in the figure...

A parallel plate capacitor in the figure 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)` .

What is the rms value of the conduction current ?

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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