Question

A radio antenna broadcasts a$1.0MHz$radio wave with $25kW$of power. Assume that the radiation is emitted uniformly in all directions.

a. What is the wave’s intensity 30 km from the antenna?

b. What is the electric field amplitude at this distance?

Short answer

(a) Waves Intensity$I_o=2.2\times {10}^{-6}\mathrm{V}/\mathrm{m}$

(b) Electric field$E_o=0.041\mathrm{V}/\mathrm{m}$

Step-by-step solution

Introduction

Antennas are considerably more than simply radio-connected gadgets. They're the transducers that turn a transmitter's voltage into a radio signal. They also pick up radio signals in the air and convert them to a voltage that can be recovered in a receiver.

Given Values:

$P=25\times {10}^3\mathrm{W}$

$d=30\times {10}^3\mathrm{m}$

$A=4\pi d^2$

Find Average Intensity

$A_{vg}$Intensity $I_o$

$I_o=\frac{P}{4\pi d^2}$

$I_o=\frac{25\times {10}^3}{4\pi {\left(30\times {10}^3\right)}^2}$

$I_o=2.2\times {10}^{-6}\mathrm{V}/\mathrm{m}$

Find Electric field

Electric field $E_p$:

$E_o={\left(\frac{2I_{avg}}{c·{\epsilon }_o}\right)}^{1/2}$

$E_o={\left(\frac{2\times 2.2\times {10}^{-6}}{3\times {10}^8\times 8.85\times {10}^{-12}}\right)}^{1/2}$

$E_o=0.041\mathrm{V}/\mathrm{m}$