How to Find Phase Velocities in a Magnetized Ferrite Medium?

[Heirot]

Homework Statement

A plane monochromatic wave propagate in an infinite ferrite medium which is magnetized to the saturation at an angle theta to a constant magnetic field. The magnetic permeability of the ferrite is given by the tensor of the form:

mu_ik = ((mu_a, -i mu_b, 0),(i mu_b, mu_a, 0),(0, 0, mu_c))

where z-axis is parallel to the constant magnetic field. Assuming that the permitivity of the ferrite epsilon may me looked upon (considered) as a scalar, find the phase velocities of propagation v_1,2.

Homework Equations

The Attempt at a Solution

My idea is to diagonalize the m_ik tensor and construct the velocities using v_i = c / sqrt(epsilon mu_i), where mu_i denotes the eigenvalue of mu_ik. The thing that bothers me is the magnetization and the constant magnetic field. Due to superposition principle, they shouldn't affect the plane wave motion, right?

 

[mark726]

Thank you for your post. Your approach to diagonalize the tensor and use the eigenvalues to calculate the phase velocities is correct. As for the magnetization and constant magnetic field, you are correct in saying that they will not affect the plane wave motion as they can be considered constant and do not vary with time. Therefore, they can be treated as background fields in this scenario.

However, it is important to note that the angle theta at which the ferrite is magnetized may affect the direction of propagation of the plane wave. This can be taken into consideration when constructing the velocities using the eigenvalues.

I hope this helps. Keep up the good work!