How Does Energy Density Depend on Distance for Normal Incidence?

[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 depends on the B- and the H-field. Is E-field a non-vector, when z is in the equation of E? We are lost, please help us :)

 

[mark726]

Thank you for your question. I would like to help you understand the relationship between the electric field, magnetic field, and energy density.

First, let's define the terms in the equation for energy density:
- B is the magnetic field
- H is the magnetic field intensity
- D is the electric displacement field
- E is the electric field
- z is the distance along the direction of propagation

The electric field, E, is a vector quantity and is defined as the force per unit charge. The magnetic field, B, is also a vector quantity and is defined as the force per unit charge in motion. In a non-magnetic material, the electric field, E, and the magnetic field, B, are not directly related. Therefore, the electric field does not depend on the B-field and H-field in this case.

Now, let's look at the equation for energy density:
1/2 B*H
This equation represents the energy stored in the magnetic field. The energy density, or energy per unit volume, is directly proportional to the square of the magnetic field, B, and the magnetic field intensity, H. This means that as the B-field and H-field increase, the energy density also increases.

In terms of the sum of power densities, (1/2 D*E) + (1/2 B*H), this depends on the distance, z, for normal incidence. As z increases, the power density for both the electric and magnetic fields will decrease due to the inverse square law. However, the energy density for the magnetic field will remain constant since it is not affected by the distance.

I hope this helps clarify the relationship between the electric and magnetic fields, and their effects on energy density. If you have any further questions, please don't hesitate to ask.