Question

An 800-kHz radio signal is detected at a point 2.7 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.36 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the average total power radiated by the transmitter

Answer 1

Explanation:

It is given that,

Frequency of radio signal, f = 800 k Hz

It is detected at a point 2.7 km distance from a transmitter tower, r = 2.7 km = 2700 m

The amplitude of electric field, E = 0.36 V/m

We need to find the average total power radiated by the transmitter. It is given by :

$P=I\times A$

I is the intensity of the radio signal, $I=\dfrac{E^2}{2\mu_o c}$

$P=\dfrac{E^2}{2\mu_o c}\times 4\pi r^2$

$P=\dfrac{(0.36)^2}{2\times 4\pi \times 10^{-7}\times 3\times 10^8}\times 4\pi (2700)^2$

P = 15746.4 watts

So, the average total power radiated by the transmitter is 15746.4 watts. Hence, this is the required solution.