Does the medium a magnetic field is propagating through affect its speed?

I'm wondering if a material's magnetic susceptibility or magnetic permeability would have an effect on the speed a magnetic field would propagate through it. I know it won't speed it up but I'm wondering if it could slow it down.

Think of a very long iron cylinder with an electromagnet on one end. It is quickly turned on and off once to send a magnetic pulse. Would this magnetic pulse travel slower than the speed of light?

I think it'd be similar to how light slows down in different materials.

• A propagating magnetic field is an electromagnetic wave.many materials from water to metals exhibit some form of magnetic susceptibility so the speed of the electromagnetic wave would depend on the material and the transparency to the wave. Commented Jul 29, 2016 at 0:31

Yes the magnetic properties will have an effect on the speed of the spread, and the phenomenon IS part of the description of how light slows down in materials. However, to see this phenomenon in this way means that we must use electromagnetic radiation of much lower frequency than visible light, because generally magnetic dipoles, owing to their relative size, react to electromagnetic fields much more slowly than electrons, hence almost always the effect is negligible at light frequencies. We also have the problem that most significantly magnetic materials are highly absorbing at visible light frequencies.

If we define the refractive index $n$ of a material to be the ratio of the freespace speed to in-material speed of light, if the material is linear and if the electromagnetic radiation is of the approriate frequency (as discussed above) then it follows directly from Maxwell's equations that:

$$n = \sqrt{\epsilon_r\,\mu_r}$$

where $\epsilon_r\,\mu_r$ are the material's relative electric and magnetic constant, respectively.

Magnetic effects are often highly nonlinear, which means the phenomenon is almost always much more complicated than discussed above. But the idea is the same: magnetic effects propagate through materials at lower than the vacuum lightspeed owing to the sloth of dipoles' reaction to the magnetic field.

If the material is working in the linear regime and loss is not significant, the effective refractive index is as I've given it above. However, with most magnetic materials, the conductivity is significant and you would need to use the general expression for the propagation constant from Maxwell's equations which is:

$$\gamma=\sqrt{i\,\omega\,\mu\,(\sigma + i\,\omega\,\epsilon)}$$

then the group velocity is $\mathrm{Re}(-i\,\frac{\mathrm{d}\gamma}{\mathrm{d}\omega})$.

• Is there a formula for the speed of magnetism in materials based off their magnetic constants and if so what is it? Commented Jul 29, 2016 at 0:52
• @Laff70 if it is in the linear regime the effective refractive index is as I've given it above. However, with most magnetic materials, the conductivity is significant so see my update above Commented Jul 29, 2016 at 1:00
• Well I'm thinking about this in the terms of the magnetic medium being laminated so it is not conductive. As a result I wouldn't have to worry about those losses. I tried doing some math and I got the equation C*(material_electric_permeability*material_magnetic_permeability)^-0.5=Speed of magnetism in material. After plugging in iron's relative magnetic permeability(5000) in I got the result of magnetism travelling 1/70 of the speed of light in iron. Commented Jul 29, 2016 at 1:12
• @Laff70 That doesn't sound unreasonable. However, I suspect your result would depend on the rise time of the pulse and it probably wouldn't be hard to check experimentally with an oscilloscope. Commented Jul 29, 2016 at 1:33
• I wasn't sure if I came up with the wrong equation so I really appreciate your verification. If I ever get an oscilloscope I'll think about testing it out. Commented Jul 29, 2016 at 1:45