# Magnetic field index of refraction

1. May 15, 2010

### mcjosep

Does a magnetic field refract when it enters into a different medium?

2. May 15, 2010

### Bob S

Yes. In going from air into a medium with permeability u at an angle, H-parallel is continuous at the boundary, and the normal component of B=uH is continuous at the boundary, so the B lines appear to "refract" as they enter the medium with permeability u. So u is the equivalent of the index of refraction in dielectrics.

Bob S

3. May 16, 2010

### DrDu

More precisely, u is the equivalent of epsilon and determines the refraction in magnetostatic situations. The refractive index determines the refraction of electromagnetic waves i.e. of both their electric and magnetic field components.

4. May 16, 2010

### Acut

Hm, the magnetic field changes direction, but it doesn't refract (in the strict sense of the word), as refraction is a wave phenomenon. Giving a easier example: when earth orbits around the Sun, it constantly changes direction, but it's not refracting. Of course, when a magnetic field is part of a electromagnetic wave, then both the wave and the magnetic field change direction (except in normal incidence, of course), but we can only say the wave has refracted. The maximum we can say about the magnetic field is that it has changed direction.

@DrDu: well, not quite.
You can say the whole wave refracts, but its constituent electric and magnetic fields don't refract, since the aren't waves. And u isn't the "refraction index" for the magnetostatic case, for the same reasons.

Last edited: May 16, 2010
5. May 16, 2010

### sophiecentaur

The question is really a bit too open, I think. "When it enters" sounds like some energy flow (i.e. wave) is involved / implied.

In any case, if not referring to a wave, why should a magnetic 'field line' not have its direction modified across a boundary? If current flow and Electric fields change, what's so unimaginable?

6. May 16, 2010

### Bob S

My earlier post referred to static magnetic field B lines crossing a magnetic boundary from one permeability to another, where my statement that the direction of the "field lines appear to "refract" " is nearly equivalent to a "Snell's Law" sin i/sin r = μ. Because this is a magnetostatic case, there is no wavelength or wave velocity involved. Because μ is usually >>1 in most magnetic materials, the magnetic field lines inside the permeable material are usually nearly perpendicular to the boundary.

Bob S

7. Jul 11, 2011

### ALAN PAYNE

Bob : I am very interested in your modified "Snell's Law" sin i/sin r = μ. How is this derived/proved ?

Alan P

8. Jul 12, 2011

### ALAN PAYNE

The 'refraction' could be Tan r/Tan i = 1/μ. See webmit.edu/6.013_book/www/chapter9/9.6.html

Alan Payne