Question

a sinusoidal electromagnetic wave has an electric field whose rms value is 100 V/m. What is the instantaneous rate S of energy flow for this wave?

Answer 1

To solve this problem it is necessary to apply the concepts related to Energy Carried by Electromagnetic Waves.

The energy calculated per unit area per unit of time that crosses a plane perpendicular to the wave is called from the theory as energy flow and is usually denoted by the letter S.

Its calculation can be developed by dividing the energy by the area in the time interval, that is:

$S = \frac{\textrm{Energy passing Area in time t} }{At} = uc = \epsilon_0 c E^2$

Where,

$c = 3*10^8 m/s \rightarrow$ Speed of light

E = Electric field

$\epsilon = 8.85*10^{-12}F/m \rightarrow$ Vacuum permittivity

From the statement we are given the value of the electric field that is 100V / m, therefore:

$S = \epsilon_0 c E^2$

$S = (8.85*10^{-12})(3*10^8)(100)^2$

$S = 26.53W/m^2$

Therefore the instantaneous rate of energy flow for this wave is $S = 26.53W/m^2$