InterviewSolution
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InterviewSolution
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A parallel plate capacitor with circular plates o f radius lm has a capacitance o f 1 nF. At 1=0, it is connected fo r charging in series with a resistor R = IM omegaacross a 2V battery. Calculate the magnetic field at a point P, halfway between the centre and the periphery o f the plates, after t = 10^(-3)s. (The charge on the capacitor at time t is q(t) = CV[1- exp (t//tau )], where the time constant tauis equal to CR) |
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Answer» Solution :The time constant of the CR circuit is `TAU = CR = 10^(-3)` s. Then, we have `q(t) = CV[l-exp(-t//tau)]` `= 2 xx 10^(-9) [1-exp (-t//10^(-3)]` The electric field in between the plates at time t is `A = PI(l)^(2) m^(2)` = area of the plates. Consider now a circular loop of radius [ 1/2) m parallel to the plates passing through P. The magnetic field B at all points on the loop is along the loop and of the same VALUE. Then flux `E xxpixx1/2^(2)=(piE)/(4)=(q )/(4epsilon_(0))` Thedisplacement current Now applyingamere maxwell law to the loopwe get or `B=0.74 xx10^(-13)` T |
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