Question

An airplane flying at a distance of 13 km from a radio transmitter receives a signal of intensity 9.2 μW/m². What is the amplitude of the (a) electric and (b) magnetic component of the signal at the airplane? (c) If the transmitter radiates uniformly over a hemisphere, what is the transmission power?

Answer 1

Part A.

Relation between Intensity and maximum electric field is given by:

I = (1/2)*c**E_max^2

E_max = sqrt (2*I/(c*))

Using given values:

E_max = sqrt (2*9.2*10^-6/(3*10^8*8.85*10^-12))

E_max = 83.25*10^-3 N/C = Amplitude of electric field

Part B.

Relation between max electric field and max magnetic field is given by:

B_max = E_max/c

B_max = 83.25*10^-3/(3*10^8)

B_max = 27.75*10^-11 T

Part C.

Power of transmitter will be:

Power = Intensity*Area

Area = Surface area of hemisphere = 2*pi*R^2

So,

P = 9.2*10^-6*2*pi*(13*10^3)^2

P = 9769.1 W

P = 9770 W = 9.77 kW

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