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Name: Gerin
Status: student
Grade: 9-12
Location: N/A
Country: N/A
Date: 1/17/2006


Question:
Hi, I am working on my Extended Essay in Physics for my IB Diploma and I am analyzing the magnetic permeability of liquids with different densities. I stumbled upon the following problem in my data processing:

From Maxwell's equation I know that,
            1
c = sqr( ------  )
         E0 Muh0

where E0 is the permitivity of free space and Muh0 is the permeability of free space.

and the index of refraction n = c/c'

So I did some arithmetic and got
      E' Muh'
n^2= -------
      E0 Muh0
Now my question is, whether the permittivity increases/decreases proportionately with the permeability? My guess would be that it does, because the electric and magnetic fields of light (electromagnetic waves) are perpendicularly in phase and one cannot "lag" behind the other upon entering a different medium. Is this correct? On the other hand, electromagnetic waves and magnetic fields are different because magnetic flux cannot be "blocked," but only diverted around or attracted to a medium as the flux takes the path of least resistance.

I would like to Graph n^2 on the x-axis against the relative permeability (Muh'/Muh0) on the y-axis. But I feel that this would only be valid if the above statement is true, which would mean that the slope of my graph is a constant (m=Eo/E').

Also, is there any (relatively) simple way/equation to find the density of a liquid from the index of refraction and vice versa?


Replies:
Gerin,

Permeability and permittivity do not have to be linked by any specific mathematical relationship. These numbers represent how a material responds to electric and magnetic fields within it.

Permittivity: An electric field causes some materials to polarize. Negative charges move toward one side and positive charges move toward the other. These produce an electric field that opposes the original field. This then reduces the total electric field within the material. Materials in which this does not happen have the permittivity of free space. In a material that ends up with a total field half that of the original field has a twice the permittivity of free space. Permittivity can often be easily measured with a capacitor.

Permeability: A magnetic field will cause a magnet to align with it. The magnetic field within the magnet is thus greater than the original field. Most materials have atoms with some magnetic properties. The three general classes of material are paramagnetic, ferromagnetic, and diamagnetic. In the first two, magnetic field within the material is greater than the original field. In a diamagnetic material, the reverse is true. A material with no magnetic properties has a permeability of free space. Paramagnetic and ferromagnetic materials have permeability greater than that of free space. Permeability is less for diamagnetic materials. Permeability, however, is seldom shifted from that of free space by more than 0.10%. Compared to permittivity, permeability has very little variance from material to material.

Of course, you must always remember that Maxwell's Equations are average effects. At the level of individual atoms, things are really quite random. Different frequencies have different permittivities and different speeds within a material. A material that responds greatly to an electric field of a certain frequency is a material with atoms that can easily absorb that frequency for a short time. When the atoms release the light, it has been delayed. A material that does NOT respond to a field has very little chance of absorbing the light. There is very little delay, if any. Some frequencies experience greater delays than others. This in turn leads to refraction. Some materials can hold the light energy long enough to completely randomize its direction. This leads to reflection. Some materials hold the energy long enough to convert it to heat energy. This is how the sun makes things warm.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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