A radio tower is broadcasting a signal with an average power of 50 kW. The energ

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. Wil 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 = POWER/AREA

    i = 10^-7/4*3.14 * 100*100 = 0.796 W/m^2

yes signal wwill be receiveed

b. at 100 km

i   = 10^-7/4*3.14 * 100*100*10^6   = 0.796 *10^-6 w/m^2

signal will not be received.

c. Erms^2 = I uoC = 0.796 *12.56*30,

    Erms = 17.31 N/C     Emax =   24.48 N/C

d. E1/E2 = r2/r1

    r2/r1 = 1000

   r2 = 1000 * 100 =    10^5 m

at a distance of 10^5 m E is 1/1000 of E at 100 m

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