# Speed of light in a superconductor

1. Jul 25, 2008

### Domenicaccio

Could you please spot where is the fault in this reasoning? I suspect that some of the relations may not be applicable and needs to be substituted with something else (or I'm just making a gross mistake as usual...):

Speed of light in a material:

$$c=\sqrt{\frac{1}{\epsilon\mu}}$$

where permettivity is

$$\mu=\mu_r\mu_0$$

and suscettivity is

$$\chi_m=\mu_r - 1$$

which describes the magnetization of the material due to an external magnetic field

$$M=\chi_m H$$

-------------------------

A superconductor behaves like a perfectly diamagnetic material, suppressing the internal field B because

$$\chi_m = - 1$$

$$M=-H$$

therefore

$$\mu_r = 0$$

$$\mu = 0$$

$$c=infinite$$

which clearly makes no sense...

2. Jul 25, 2008

### yoyoq

there are also negative index of refraction materials
which also mess that up.

i think the subtlety is the phase vs group velocity
of the light waves.

http://en.wikipedia.org/wiki/Phase_velocity

"...The phase velocity of electromagnetic radiation may under certain circumstances (e.g. in the case of anomalous dispersion) exceed the speed of light in a vacuum, but this does not indicate any superluminal information or energy transfer..."

Last edited: Jul 25, 2008
3. Jul 25, 2008

### Ben Niehoff

Also, in a perfect conductor, $\epsilon = \infty$. I don't know if this applies to superconductors (but they do offer practically zero resistance, yes?).

4. Jul 25, 2008

### kanato

IIRC, the penetration depth of light into a conductor is proportionate to the resistivity, so in a perfect conductor light won't penetrate at all (the charge carries at the surface absorb all the light that isn't reflected).

5. Jul 26, 2008

### Vanadium 50

Staff Emeritus
What you are discovering is that you don't have electromagnetic radiation inside an ideal superconductor.

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