Question

24.45 - Energy in Electromagnetic Waves A 180-turn flat coil of wire 35.0 cm in diameter acts as an antenna for FM radio at a frequency of 120 MHz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of 1.01x1012 T. what power is incident on the coil? Submit Answer Tries o/10 What average emf is induced in the coil over one-fourth of a cycle? Submit Answer Tries 0/10 If the radio receiver has an inductance of 2.10 μΗ, what capacitance must it have to resonate at 120 MHz? Submit Answer Tries o/10

Answer 1

Given data are: No. of turns (N) = 180 diameter (d) = 35 cm = 0.35 m radius (r) = 0.175 m frequency (f) = 120 MHz magnetic field (B) = 1.01 times 10^-12 T (a) power will b p = I times A p = CB^2/2 mu_0 times pi r^2 = (3 times 10^8) (1.01 times 10^12)^2 times pi (0.175)^2/2 times 4 pi times 10^-7 p = 0.011715 times 10^-9 w p = 11.715 times 10^-12 w (or) p TildeEqual 11.72 pw (b) We have EMF = N d phi/dt E = NA dB/dt E = NA dB/T/4 = 4 NAdB/T rightarrow (1) We have T = 1/f = 1/120 times 10^6 = 8.33 ns Therefore from eqn (1) E = 4 times 180 times pi (0.175)^2 times (1.01 times 10^-12)/8.33 times 10^-9) E = 8.3991 times 10^-3 v (or) E = TildeEqual 8.4 mV \r\n (c) given L = 2.10 MH & f = 120 MH