# Switching polarity on electromagnets

1. May 15, 2012

### dorker

First off, hi, I'm new. Sorry if this is not the right board; I was unsure between Classical Physics, maybe Quantum since this involves fields, or Electrical Engineering.

On to the question, say you have an electromagnet with an iron core. As I understand it, a magnetic field acts on a ferromagnetic material by aligning the magnetic spin of the latter's atoms. If you were to switch the electromagnets' polarity back and forth, can I assume this magnetic alignment propagates through the core instantly (or at the speed of light would more correct, I suppose), or are there any dynamic equations for this kind of thing?

And if it is an "instantaneous" effect, is there anything limiting the frequency I can switch the polarity with, or can I go as fast I want and assume the iron can take it?

2. May 16, 2012

### M Quack

The magnetic field penetrates the material at the speed of light (in the material, which may be lower than the speed of light in vacuum), but the magnetization does not follow instantaneously.

In general, you don't flip the spins one by one, but you flip little domains. These can be pinned, i.e. you need a certain field strength to change their alignment. So the magnetization proceeds in little jumps that can be measured. If you attach a pick-up coil and headphones it can even be heard. This is called Barkhausen noise.

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

Another frequency limiting effect is that magnet cores tend to be metallic. A changing magnetic field therefore induces an electric current (Eddy current) in the core that leads to losses in the form of heat. The induced currents depend on the rate of change of the magnetic field, so that at higher frequency the losses are higher.

Check out the section on energy losses here:
http://en.wikipedia.org/wiki/Transformer

3. May 16, 2012

### dorker

Thanks. Is that what the Landau-Lifgarbagez-(Gilbert) equation is about?

4. May 16, 2012

### Bob S

True.
The wave equation for H(x,t) is given by
$$\frac{\partial^2H\left(x,t \right)}{\partial x^2}-\epsilon \mu \frac{\partial^2H\left(x,t \right)}{\partial t^2} = 0$$
where the speed of H(x,t) is given by $v=\frac{1}{\sqrt{\epsilon \mu}}$. In soft magnetic materials, μ is $very$ high, meaning that the magnetization wave is $\sqrt{very}$ slow.

5. May 16, 2012

### M Quack

$\sqrt{\mathrm{very}}$ ... I love that one.

Note that your equation is for the continuum approximation and assuming that the magnetization is proportional to the applied field. If you have domains jumping back and forth this is no longer correct - you get hysteresis and locally non-uniform magnetization.

6. May 16, 2012

### dorker

Thanks to everyone for the answers, but Bob S, could you clear up a couple of things for me? First, the H in that equation is the magnetic field, right? So why do you say this means the magnetization propagates slowly?

Second, what's the source on that equation? Thanks.

Last edited: May 16, 2012
7. May 17, 2012

### M Quack

The problem is that there are two "magnetic fields", H and B. Roughly speaking, H does not include the response of the material, and B does include it.

When the material response is linear one can write $B = \mu \mu_0 H$. This is pretty much always the case when talking about electromagnetic waves, hence the formula for the speed of light. When talking about ferromagnets the response becomes non-linear and things get more complicated.

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

The equation is the electromagnetic wave equation, derived from Maxwell's equations.

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