An airplane flying at a distance of 8.3 km from a radio transmitter receives a signal of intensity 15 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?

a) Amplitude of the electric field, E = 0.1063 V/m

b) Magnetic field, B = = 3.545 x 10⁻¹⁰ Tesla

c) Transmission power, P = 6492.73 W

Explanation:

Intensity, I = 15 μW/m²

Distance, R = 8.3 km = 8300 m

a) The electric field amplitude  

Relationship between the amplitude and intensity of a signal is given by:

..........(1)

c = 3 * 10⁸ m/s

μ = 4 π * 10⁻⁷

Substitute these values into equation (1)

b)Amplitude of the magnetic field component at the airplane

 B = E / c

B = = 0.1063 / (3 x 10⁸ )

B = = 3.545 x 10⁻¹⁰ Tesla

3) The transmission power:

Intensity,

 P = I A

Area of the hemisphere, A = 2πR²

A = 2π * 8300²

A = 432848635.8116 m²

Power, P = 15 * 10⁻⁶ * 432848635.8116

P = 6492.73 W