Radio station WCCO in Minneapolis broadcasts at a frequency of 830 kHz . At a po

Question

Radio station WCCO in Minneapolis broadcasts at a frequency of 830 kHz . At a point some distance from the transmitter, the magnetic-field amplitude of the electromagnetic wave from WCCO is 4.74×1011 T

Part A

Calculate the wavelength
lambda=_________m


Part B

Calculate the wave number.
k=__________rad/m


Part C

Calculate the angular frequency
w=__________rad/s


Part D

Calculate the electric-field amplitude
E=___________V/m

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Explanation / Answer

a) for any wave, velocity = frequency * lambda

for radio wave v = c

wavelength(lambda) = c / frequency = 3 x 10^8 / (830 x 10^3)

       = 361.45 Hz

b) Wave number k = 2pi / wavelength

k = 2 x pi / 361.45 = 0.017 rad/m

c) angular frequency w = 2 pi f
w = 2 x pi x 830 x 10^3 = 5.21 x 10^6 rad/s

d) for an electromagnetic wave, the amplitude of the electric is c times the amplitude of the magnetic fiels :

E0 = cB0 = 3 x 10^8 x 4.74 x 10^-11 = 0.0142 V/m

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