# Permeability, permittivity and susceptibility

1. Jun 28, 2011

### luitzen

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.

Last edited: Jun 28, 2011
2. Jun 28, 2011

### Born2bwire

\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.

3. Jun 28, 2011

### luitzen

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.

4. Jun 28, 2011

### Blibbler

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.

5. Jun 28, 2011

### luitzen

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.