Question

An electromagnetic wave has an electric field component varying with position x and time t defined as E=E0​cos(kx−ωt). Find the intensity of the wave.

Answer 1

The intensity of an electromagnetic wave with an electric field variation of E=E0​cos(kx−ωt) is calculated using the relationship that intensity is proportional to the square of the amplitude of the electric field, resulting in I = E0^2/(2ε₀0c).

Step-by-step explanation:

To find the intensity of an electromagnetic wave with an electric field component varying as E = E0​cos(kx−ωt), we can use the relationship that the intensity (I) of a wave is proportional to the square of its amplitude. Here, E0 is the amplitude of the electric field. By using the average intensity of an electromagnetic wave in terms of the electric field, we get the relationship Iave = (E0^2/2ε₀0c).

It's also important to remember that the intensity relates to the maximum electric field as Iave = (E^2₀/ε₀0c), where c is the speed of light, and ε₀0 is the permittivity of free space. We use the fact that the average of cos^2 is 1/2 over a complete cycle. Hence, the intensity of the wave is I = E0^2/(2ε₀0c).