Question

A plane electromagnetic wave varies sinusoidally at 86.0 MHz as it travels through vacuum along the positive x-direction. The peak value of the electric field is 2.30 mV/m, and it is directed along the positive y-direction. Determine the average power per unit area (the intensity) this wave carries through space. (Be careful with your units here and make sure to submit your answer in μW/cm2)

Answer 1

Answer:

The intensity is  $I = 0.0003053 \mu W/cm^2$

Explanation:

 From the question we are told

     The  frequency of the electromagnetic wave is  $f = 86.0 Hz$

     The peak value of the electric field is  $E_o = 2.30 mV/m = \frac{2.30}{1000 } = 2.30 *10^{-3} V/m$

         

Generally  the intensity of this wave is mathematically represented as

     

                $I = c * \frac{1}{2} * \epsilon_o E^2_o$

Where c is the speed of light with value  $c = 3 *10^8 m/s$

           $\epsilon_o$ is the permittivity of free space with value  $\epsilon _o = 8.85 *10^{-12} C^2 /Nm^2$

Substituting values into equation for intensity

               $I = 3.0 *10^8 * 0.5 * 8.85 *10^{-12} * 2.30*10^{-3}$

                 $I = 3.053 *10^{-6} W/m^2$

Converting to $cm^2$ we divide by 10,000

                $I = \frac{3.053 *10^{-6}}{10000} W/cm^2$

                $= 3.053 *10^{-10} W/cm^2$

                $= 0.0003053 *10^{-6} W/cm^2$

                $I = 0.0003053 \mu W/cm^2$