Permeability, permittivity and susceptibility

  1. I got a little confused of these three things by my teacher and Griffiths.

    I am acquaintanced with Feynman's lectures on physics and what I get from there is [itex]\epsilon=\epsilon_{r}\epsilon_{0} = \left(1+\chi\right)\epsilon_{0}[/itex]

    For some reason Griffiths, as well as my teacher, likes to use [itex]\mu_{0}[/itex], where [itex]\mu_{0} = \dfrac{1}{\epsilon_{0}c^{2}}[/itex].

    Now I'd assume [itex]\mu=\dfrac{1}{\epsilon c^{2}}[/itex] and thus [itex]\mu=\dfrac{1}{\epsilon_{r}\epsilon_{0}c^{2}} = \dfrac{1}{\epsilon_{r}}\mu_{0}=\left(1+\chi\right)^{-1}\mu_{0}[/itex]

    But apparently (Wikipedia, Griffiths, etc.) [itex]\mu=\left(1+\chi\right)\mu_{0}[/itex]

    So what should it be?

    And why do they use [itex]\mu[/itex] at all? It seem rather inconvenient to me, since they keep writing stuff like [itex]\sqrt{\dfrac{1}{\epsilon_{0}\mu_{0}}}[/itex] instead of c.
     
    Last edited: Jun 28, 2011
  2. jcsd
  3. Born2bwire

    Born2bwire 1,776
    Science Advisor
    Gold Member

    \mu and \epsilon are different things. Permittivity is related to the material response to an applied electric field. Permeability is related to the material response to a magnetic field. They do not share the same susceptibility and only in free space can you assume that the product of the two is equal to c^-2.
     
  4. Ok, thank you very much.

    Then I think I'm gonna stick with [itex]\mu[/itex] for the test and find out what it exactly means later.
     
  5. Don't you find it beautiful that c is defined as the reciprocal of the square root of the product of two truly fundamental constants of nature?

    That identity tells you what c is - it's the speed at which an electromagnetic wave can propagate through free space and it is governed only by the electrical permittivity and the magnetic permeability of free space.

    I find it jaw dropping.
     
  6. I always saw the speed of light as something that was just known and I thought that permeability was used because it showed up often with permittivity and physicists are lazy. Now I realize that permeability and permittivity are something entirely different. That doesn't mean I now understand what it means, but it's at least a start.

    I just started reading a book "Space, time and relativity" by Engel Roza and now I also know that the speed of light was first determined, by Maxwell, using [itex]\mu_{0}[/itex] and [itex]\epsilon_{0}[/itex]

    PS does anyone know why my TeX isn't displayed correctly in my first post? I can't find a mistake, but maybe someone else can.
    PPS adding spaces did miracles.
     
    Last edited: Jun 28, 2011
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