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

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

Step-by-step 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 = (2.30)/(1000 ) = 2.30 *10^(-3) V/m`

Generally the intensity of this wave is mathematically represented as

`I = c * (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 = (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`