Why permeability equal to unity?

[iLIKEstuff]

I apologize if this is not in the correct section of the forum, but it seems most fitting.

In the context of dielectric materials, I am having trouble understanding why in the discussion of the optical properties of magnetized bodies, it is justifiable to assume for light vibrations, permeability = 1.

I have read several texts stating that this is an assumption but I do not understand the physical basis of making such an assumption. One texts simply states, "The reason for this is not that the magnetization of a body cannot follow the rapid changes of field which occur in light vibrations, but is far more complicated." and then follows with some daunting deriviations of equations describing the EM field in a dielectric body. It also states that "in dielectrics, permeability differs so little from 1 (generally only a few thousandths of 1%) that in what follows it will always be considered equal to 1."

I know that the permeability of free space is 4*pi*10^-7 = 1.2566*10^-6 N/A^2 (SI units) and that free space (vacuum) is a dielectric. So, where are they getting "permeability differs so little from 1"
Thanks guys.

 

[pam]

They are either talking about the relative permeability (mu/muzero) in SI or the permeability
in the gaussian system of units, each of which is 1 in most dielectrics.
You wrote "the permeability of free space is 4*pi*10^-7 = 1.2566*10^-6 N/A^2 (SI units)".
$$\mu_0/4\pi=10^{-7}$$ is not an experimental number. It would equal 1 in emu (cgs) units. Its value in SI comes about because SI uses mks, and the SI ampere was taken to be equal to 0.1 abamperes

 

[denian]

Thank you for bringing up this question regarding the assumption of permeability equal to unity in the discussion of optical properties of magnetized bodies. I can understand your confusion and would like to provide some insights on this topic.

Firstly, I would like to clarify that this assumption is specific to dielectric materials, which have different properties compared to free space or vacuum. In dielectrics, the permeability is a complex quantity that depends on the frequency of the electromagnetic field. Therefore, it is not a constant value like in free space. However, at optical frequencies, the changes in permeability for dielectric materials are very small, typically on the order of a few thousandths of 1%. This is why it is often considered to be equal to 1 in discussions of optical properties.

To understand the physical basis of this assumption, we need to look at the microscopic behavior of the electrons in a dielectric material. In the presence of an electromagnetic field, the electrons in the material will experience a force and start to oscillate. These oscillations contribute to the overall response of the material to the electromagnetic field. However, at optical frequencies, the oscillations of the electrons are not fast enough to keep up with the rapidly changing field, and thus their contribution to the permeability is negligible. This is why it is justified to assume permeability equal to unity in the context of optical properties of dielectric materials.

I hope this helps to clarify the reasoning behind this assumption. It is important to note that this is a simplification and may not hold true for all dielectric materials or at all frequencies. It is always best to consider the specific properties of the material in question when studying its optical properties.

Best regards,