A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The

Question

A flat coil of wire is used with an LC-tuned circuit as a receiving antenna. The coil has a radius of 0.35 m and consists of 440 turns. The transmitted radio wave has a frequency of 1.2 MHz. The magnetic field of the wave is parallel to the normal to the coil and has a maximum value of 2.0 10-13 T. Using Faraday's law of electromagnetic induction and the fact that the magnetic field changes from zero to its maximum value in one-quarter of a wave period, find the magnitude of the average emf induced in the antenna during this time.
V

Please provide explanation and answer.

Explanation / Answer

number of turns N = 440
area of the coil A = r2 = 3.14*0.35*0.35 frequency f = 1.2*106 Hz magnetic field B = 2*10-13 T
amplitude of magnetic field, time to go from zero to B is          dt = T/4 = 1/4f   ............ (1)    (since T = 1/f) using Faraday's law , the average emf = d/dt                        = NAB/dt     ............ (2) the magnitude of the average emf induced in the antenna during this time is
     Vav = NAB/(1/4f)            = 4NABf
     Vav = N*A*B*4f
           = 440*3.14*0.35*0.35*2*10-13*4*1.2*106
           = 16.247*10-5 V

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