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.
\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.
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.
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.
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.