Public television station KQED in San Francisco broadcasts a sinusoidal radio si

Question

Public television station KQED in San Francisco broadcasts a sinusoidal radio signal at a power of 316 kW. Assume that the wave spreads out uniformly into a hemisphere above the ground.

A.At a home 6.00km away from the antenna, what average pressure does this wave exert on a totally reflecting surface?

B.At a home 6.00km away from the antenna, what are the amplitudes of the electric and magnetic fields of the wave?

C.At a home 6.00km away from the antenna, what is the average density of the energy this wave carries?

D.For the energy density in part (c), what percentage is due to the electric field?

E.For the energy density in part (c), what percentage is due to the magnetic field?

Explanation / Answer

power of the signal is P = 316 KW = 316 * 103 W

Distance between transmitter and antenna R = 6.00 km = 6 * 103 m

A) Intensity of signal I = P / A = P / 2 pi r2 =   316 * 103  / ( 2 pi (6 * 103)2)

= 1.39 * 10-3 W/m2

p = 2 I / c = (2 * 1.39 * 10-3) / (3 * 108)

= 9.26 * 10-12 pa

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B) Emax =sqrt [2 I / e0 c]

= sqrt [2 * 1.39 * 10-3 / (8.85 * 10-12 * 3 * 108)]

= 1.02 V/m

AMplitude of magnetic field Bmax = Emax / c = 1.02 / 3 * 108

= 3.4 * 10-9 T

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C)The average density of energy

u = e0 [Emax / sqrt[2]]2

u = 8.85 * 10-12 [1.02 / sqrt[2]]2

= 4.60 * 10-12 W/m2

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D) E = 50%

E) B = 50%

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