Question

A)If the rms value of the electric field in an electromagnetic wave is doubled, by what factor does the rms value of the magnetic field change? B)If the rms value of the electric field in an electromagnetic wave is doubled, by what factor does the average intensity of the wave change?

Answer 1

A) The magnetic field doubles as well

The relationship between rms value of the electric field and rms value of the magnetic field for an electromagnetic wave is the following:

$E_{rms}=cB_{rms}$

where

E_rms is the magnitude of the electric field

c is the speed of light

B_rms is the magnitude of the magnetic field

From the equation, we see that the electric field and the magnetic field are directly proportional: therefore, if the rms value of the electric field is doubled, then the rms value of the magnetic field will double as well.

B) The intensity will quadruple

The intensity of an electromagnetic wave is given by

$I=\frac{1}{2}c\epsilon_0 E_0^2$

where

c is the speed of light

$\epsilon_0$ is the vacuum permittivity

$E_0$ is the peak intensity of the electric field

The rms value of the electric field is related to the peak value by

$E_{rms}=\frac{E_0}{\sqrt{2}}$

So we can rewrite the equation for the intensity as

$I=c\epsilon_0 E_{rms}^2$

we see that the intensity is proportional to the square of the rms value of the electric field: therefore, if the rms value of the electric field is doubled, the average intensity of the wave will quadruple.