In this problem we will revisit the magnetic and electric field inside a charging capacitor. You have already worked on

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In This Problem We Will Revisit The Magnetic And Electric Field Inside A Charging Capacitor You Have Already Worked On 1 (59.21 KiB) Viewed 28 times

In this problem we will revisit the magnetic and electric field inside a charging capacitor. You have already worked on this in QP15 on HW #7. The capacitor consists of two circular metal plates of radius R separated by a distance D. To refresh your memory, the capacitor is being charged by a steady current I. Charge is building up uniformly on the plates. The magnitude of the electric field between the plates is E = It/TRE where t is time and R is the radius of the plates. The magnetic field magnitude, for r<R, is B = Hor/2nR? a) What is the capacitance C? b) Find the energy Ue stored in the electric field inside the capacitor at time t. Express your answer in terms of the current I, the capacitor dimensions, the time t, and € c) The Poynting vector is defined as S = (Ex B)/po. In what direction does S point in the gap of the capacitor? d) Find the magnitude of the Poynting vector in the gap at the edge of the capacitor, i.e. at r= R. e) Using the Poynting vector, find the total amount of energy flowing into (or out of) the gap of the capacitor. ) Using the results of b) and e), show that the time rate of change of Up is exactly matched by the total energy flux implied by S.