Question

A helicopter flying at a distance of 20.0 km from a radio transmitter receives a signal of intensity 35.1 μW/m2.

A) Find the magnitude of the electric component of the signal at the helicopter’s location.

B) Find the magnitude of the magnetic component of the signal at the helicopter’s location.

C) If the radio transmitter radiates its signal uniformly over a hemisphere, what is the transmitted power?

Answer 1

a) 0.162 V/m

b) 0.54 nT

c) 22 kW

Step-by-step explanation:

Given

Distance of flight, d = 20 km

Intensity of signal, I = 35.1 μW/m²

Magnitude of the electric component is gotten using the formula

E(m) = √(2Iμc), where

E(m) = √(2 * 35*10^-6 * 4*3.142*10^-7 * 3*10^8)

E(m) = √(2 * 35*10^-6 * 1.257*10^-6 * 3*10^8)

E(m) = √0.0264

E(m) = 0.162 V/m

Magnitude of magnetic component can be gotten by using the relation

B(m) = E(m) / c

B(m) = 0.162 / 3*10^8

B(m) = 5.4*10^-10

B(m) = 0.54 nT

Transmission power, P = IA

where A = 1/2 * 4πr²

P = 2Iπr²

P = 2 * 35*10^-6 * 3.142 * (10000)²

P = 2 * 35*10^-6 * 3.142 * 1*10^8

P = 21994 W

Thus, the transmission power is 22 kW