An AM radio station broadcasts at 750 kHz. a) What is the wavelength of the radi

Question

An AM radio station broadcasts at 750 kHz. a) What is the wavelength of the radio wave in air? b) If the radio wave is tuned to this station and the inductance circuit is 0.10 mH, what is the capacitance in the tuning circuit? c) In the vicinity of the radio, the amplitude of the electric field is 040 V/m. The radio uses a coil of radius 1.8 cm with 60 turns. What is the maximum emf induced in the coil, assuming that it oriented for best reception? Assume that the electric fields are sinusoidal functions of time.

Explanation / Answer

a)

frequency of AM , f = 750 KHz

Now, wavlength = speed of light/f

wavlength = 3 *10^8/(750 *10^3)

wavlength = 400 m

the wavelength of AM is 400 m

b)

as f = 1/(sqrt(L*C) * 2pi)

750 *10^3 = 1/(2pi*sqrt(0.10 *10^-3 * C ))

solving for C

C = 4.503 *10^-10F

the capacitance needed is 4.503 *10^-10 F

C)

emf induced = 0.40 * 2*pi*f * N * area/c

emf induced = 0.40 * 2*pi* 750 *10^3 * 60 * pi*0.018^2 /3 *10^8

emf induced = 3.84 *10^-4 V

the emf induced in the coil is 3.84 *10^-4 V

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