Radio station WVBR broadcasts at 93.5 MHz from atop Hungerford Hill, with a radi

Question

Radio station WVBR broadcasts at 93.5 MHz from atop Hungerford Hill, with a radiated power of 3 kW.
(a) What is the wave intensity in Collegetown, a distance of 2 km away? (Assume the power is uniformly radiated into a sphere.)

(b) What are the magnitudes of the electric and magnetic fields in Collegetown?
(c) How much energy will flow through a 1.0 m2 Collegetown window in 1 second? (Assume the window is perpendicular to the direction of propagation.)
(d) Nicola Tesla proposed to transmit electric power not using wires but by simply broadcasting it via sinusoidal EM waves. Suppose that you wanted to transmit the power carried by a modern transmission line

Explanation / Answer

Part A)

Intensity = P/A

I = (3000)/(4pi)(2000)^2

I = 5.97 X 10^-5 W/m^2

Part B)
I = E^2/2uc

5.97 X 10^-5 = E^2/(2)(4pi X 10^-7)(3 X 10^8)

E = .212 N/C

c = E/B

(3 X 10^8) = .212/B

B = 7.07 X 10^-10 T

Part C)
I = P/A

P = IA = (5.97 X 10^-5)(1) = 5.97 X 10^-5 W

E = Pt = 5.97 X 10^-5(1) = 5.97 X 10^-5 J

Part D)
P = IV = (1000)(500000) = 5 X 10^8 W

I = P/A = 5 X 10^8/100 = 5 X 10^6 W/m^2

5 X 10^6 = E^2/2(4pi X 10^-7)(3 X 10^8)

E = 61400 N/C

c = E/B

3 X 10^8 = 61400/B

B = 2.05 X 10^-4 T

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