# Permeability, permittivity and susceptibility

by luitzen
Tags: permeability, permittivity, susceptibility
 P: 49 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 $\epsilon=\epsilon_{r}\epsilon_{0} = \left(1+\chi\right)\epsilon_{0}$ For some reason Griffiths, as well as my teacher, likes to use $\mu_{0}$, where $\mu_{0} = \dfrac{1}{\epsilon_{0}c^{2}}$. Now I'd assume $\mu=\dfrac{1}{\epsilon c^{2}}$ and thus $\mu=\dfrac{1}{\epsilon_{r}\epsilon_{0}c^{2}} = \dfrac{1}{\epsilon_{r}}\mu_{0}=\left(1+\chi\right)^{-1}\mu_{0}$ But apparently (Wikipedia, Griffiths, etc.) $\mu=\left(1+\chi\right)\mu_{0}$ So what should it be? And why do they use $\mu$ at all? It seem rather inconvenient to me, since they keep writing stuff like $\sqrt{\dfrac{1}{\epsilon_{0}\mu_{0}}}$ instead of c.
 PF Patron Sci Advisor P: 1,717 \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.
 P: 49 Ok, thank you very much. Then I think I'm gonna stick with $\mu$ for the test and find out what it exactly means later.
P: 57

## Permeability, permittivity and susceptibility

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.
 P: 49 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 $\mu_{0}$ and $\epsilon_{0}$ 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.

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