Permitivity and Permeability
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,
c = sqr( ------ )
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
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?
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
Illinois Central College
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Update: June 2012