Question

At a distance of 10 km from a radio transmitter, the amplitude of the E-field is 0.20 volts/meter. What is the total power emitted by the radio transmitter

Answer 1

Answer:

The total power is  $P = 6.665 *10^{4} \ W$        

Explanation:

From the question we are told that

     The distance is  $r = 10 \ km = 1000 \ m$

      The amplitude of the electric field is   $E = 0.20 \ volt/meter$

Generally the average intensity of the electromagnetic field from the radio transmitter is mathematically represented  as

           $I = \frac{E^2}{ 2 \mu_o * c }$

Here c is the speed of light with value  $c = 3.0 *10^{8} \ m/s$

         $\mu_o$ is the permeability of free space with value  $\mu_o = 4\pi *10^{-7} \ N/A^2$

So

           $I = \frac{0.2^2}{ 2 * 4\pi *10^{-7} * 3.0*10^{8} }$      

=>        $I = 5.307 *10^{-5} \ W/m^2$

Generally this intensity can also be mathematically represented as

               $I = \frac{P }{ 4 \pi r^2 }$

=>           $P = I ( 4 \pi r^2 )$        

=>           $P = 5.307 *10^{-5} ( 4 * 3.142 * 1000^2 )$        

=>           $P = 6.665 *10^{4} \ W$