The emitting antenna of a 100-kW radio station radiates equally in all direction

Question

The emitting antenna of a 100-kW radio station radiates equally in all directions.

A.For the distance of 700 m from the antenna, calculate the maximum potential difference caused between the ends of a receiving antenna that is 1.0 m long, assuming the antenna is aligned perfectly with the electric field of the radio wave.

B.What is the magnitude Emax 40 km from the antenna?

C.What is the magnitude Bmax 40 km from the antenna?

D.For the distance of 40 km from the antenna, calculate the maximum potential difference caused between the ends of a receiving antenna that is 1.0 m long, assuming the antenna is aligned perfectly with the electric field of the radio wave.

Explanation / Answer

A)formula for intensity

I = P/A = P/ 4 pi r^2

= 100000W/ 4 pi ( 700)^2 = 0.016 E/m^2

E max = sqrt 2 uo cI

= sqrt 2 ( 4pi * 10^-7) ( 3 * 10^8) ( 0.0162)

=3.49 V/m

V max = E max d = 3.49 ( 1.0 m) = 3.49 V

(B)

I = P/A = P/ 4 pi r^2

= 100000W/ 4 pi ( 40000)^2 = 4.97 * 10^-6 E/m^2

E max = sqrt 2 uo cI

= sqrt 2 ( 4pi * 10^-7) ( 3 * 10^8) ( 4.97 * 10^-6)

=0.0611V/m

(c)

B max = E max/c = 0.0611 V/m/ 3.0 * 10^8 = 2.03 * 10^-10 T

(D)

V max = E max d = 0.0611( 1.0 m) = 0.0611V

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