A radio tower is broadcasting a signal with an average power of 50 kW. The energ
ID: 2100930 • Letter: A
Question
A radio tower is broadcasting a signal with an average power of 50 kW. The energy is radiated uniformly in all
the directions. You are driving in a car, radially away from the radio tower with a receiver which can receive radio
signals with intensity 10^-7 W/m^2 and higher.
a) Will you be able to receive the radio signal at a distance of 100 m?
b) Will you be able to receive the radio signal at a distance of 100 km?
c) What is the amplitude of the electric field of the signal at a distance of 100 m?
d) At what distance is the magnitude of the electric field of the signal reduced to 1/1000 of its value
found at 100 m?
Explanation / Answer
a. intensity = pwer/Area = 50000/4 *3.14* 100*100 = 0.39 , YES
b. intensity = pwer/Area = 50000/4 *3.14* 10^10 = 3.9 * 10^-7, negligible intenisty so answer is N0.
c. Erms^2 = IuoC = 0.39 * 4pi *10^-7 * 3*10^8 = 147
Erms = 12.12 N/c Emax = 17.14 N/c
d. 1/1000 of 0.39 = 0.39 *10^-3
aREA = POWER/INTENSITY = 50000/0.39 *10^-3
R^2 = 1.28 *10^8
R = 1.13 *10^4 = 11.3 Km