How Does Energy Density Vary with Normal Incidence in Non-Magnetic Materials?

[Smorte]

Homework Statement

Calculate the energy density for the magnetic field (1/2 B*H) for normal incidence. The materials are non-magnetic. How does the sum of power densities (1/2 D*E) + (1/2 B*H) depend on z for normal incidence?
The parenteses are the time average, I just can't make the sign. $$\left\langle$$

Homework Equations

The electric field is E = sin(wt-kz), how does the electric field depend on B-field and H-field for a non-magnetic material?

The Attempt at a Solution

Since we don't know how the E-field depend on the B- and H-field. The E-field is a non-vector, or the z value is in the E equation. We are lost!

 

[BigJDubs]

For normal incidence, the E-field is a function of z. The B-field and H-field can be calculated from the E-field. Therefore, the energy density for the magnetic field (1/2 B*H) for normal incidence can be calculated as: 1/2 B*H = 1/2 E^2z^2 cos^2(wt-kz). The sum of power densities (1/2 D*E) + (1/2 B*H) will depend on z as: 1/2 D*E+1/2 B*H = 1/2 E^2z^2 cos^2(wt-kz) + 1/2 E^2z^2 cos^2(wt-kz).