Question

Use the complex forms for the electric and magnetic fields of an electromagnetic plane wave in a linear dielectric material with permittivity ε and permeability μ to find the ratio of the energy density stored in the oscillating magnetic field to the energy density stored in the oscillating electric field.

Answer 1

Energy density in an electric field is energy density in a magnetic field is .

An electromagnetic wave has both electric and magnetic fields, so the total energy density associated with an electromagnetic wave is:

It turns out that for an electromagnetic wave, the energy associated with the electric field is equal to the energy associated with the magnetic field, so the energy density can be written in terms of just one or the other:

This also implies that in an electromagnetic wave, E = cB. That is the ratio of energy density is c