Speed of Magnetic Field in Soft Iron: An Experiment

[Ted1]

How fast does a magnetic field travel in a magnetic material like soft iron? Not an electromagnetic wave, a magnetic field. I don't need a precise answer, the qualitative behavior is what I am after.

A thought experiment:

Imagine I have on a wooden bench a piece of conducting but unmagnetized iron rail road track 10 feet long.

I have a very strong permanent magnet that I shall attach to one end of the rail (very quickly) to make a step change in the magnetic field in the rail.

At the other end of the rail is a regular compass as a magnetic detector, the needle swings towards the rail end indicating when it has become magnetized.

To start the experiment I attach the permanent magnet at one end of the rail, some time later the compass needle announces the arrival of the magnetic field at the far end.

Question 1: What approximately is the time delay between the attachment of the PM at one end and motion of the compass needle at the other? Is it proportional to the magnetic permeability of iron? of air? To the speed of sound in iron? To the speed of light? What?

If the compass needle doesn't work for you, substitute some other magnetic sensor like a coil of wire wrapped around the rail end and attached to a galvanometer perhaps.

Question 2: What would be the difference if I substituted for the 10 foot iron rail a 10 foot rail made out of a non-conducting magnetic material like commercial "soft" ferrite? Would the step change propogate up the rail faster or slower?

Ted

 

[Integral]

So why are you asking instead of doing? Do and tell us what you learn.

 

[Ted1]

additional responses are welcome, this is a thought experiment :-)

 

[davenn]

additional responses are welcome, this is a thought experiment :-)

we are all awaiting your report of your experiments


Dave

 

[sigma_]

Is this guy expected to go out and buy a long metal rod just to verify his thought experiment? No one wants to give him an answer?

On the other hand though, a thought experiment is typically something that would be impossible or nearly impossible to create in a lab setting, i.e. Einstein's elevator thought experiment (sending someone into deep space in a frictionless, rotationless elevator probably wasnt possible in those days...or now). Your idea isn't really a thought experiment.

Anyway:

I would assume the magnetization of the opposite side of the rail would occur somewhat more slowly than the speed of an EM wave propagating through metal, and much faster than a sound wave propagating through metal.

 

[davenn]

Is this guy expected to go out and buy a long metal rod just to verify his thought experiment? No one wants to give him an answer?

not necessarily ... but he could easily get some lengths of rod and do some practical experiments

its generally a really good way to learn
and he's going to learn a lot more than just thinking about the problem


Dave

 

[sigma_]

not necessarily ... but he could easily get some lengths of rod and do some practical experiments

its generally a really good way to learn
and he's going to learn a lot more than just thinking about the problem


Dave

I agree with you, it's by far the best way to learn, but that can be cost prohibitive to some people, especially if he's young. We don't want PF to come off as unwilling to help, if that's the case.

 

[Ted1]

davenn: sorry to disappoint you but there aren't going to be any experimental results :-)

sigma_ thank you, my intuition and weak grasp of the principals tells me something similar to your conclusion, not as fast as light, but faster than sound in the solid. What I am calling a magnetic wave step change is an invention that may not exist in reality, in which case I hope someone will let me know :-)

We know the propagation of an EM wave down a conductor is affected by the permeability of the surroundings. Would the speed of a purely "magnetic wave", if such a thing exists, be similarly affected by the surroundings? And would it be faster or slower when the magnetic medium is non-conducting (ferrite) rather than conducting (iron)?

I have some further thoughts however about the thought experiment setup:

with a short iron bar the response time of a compass is too slow to be useful, so there is a refinement for a more realistic thought experiment:

a precision interval timer is employed at the (left hand) end of the rail and it is started by an optical sensor that detects when the permanent magnet contacts the end of the iron rail. At the other (right hand) end of the rail a Hall effect sensor is employed to detect arrival of the step change in magnetic field, the sensor is connected back to the interval timer (via a high speed electrical link) and operates the stop control of the interval timer. Also, the bar is increased in length so that it is long enough that it is possible to discriminate with reasonable accuracy, and using the affordable interval timer, between different propogation speeds for example the speed of sound in iron and the speed of light.
Presuming the magnetic step change I have imagined actually occurs in the iron, then as it moves up the rail, there is a moving magnetic field, and the iron is a conductor, and so there is self-inductance that opposes the magnetic field, possibly in the form of a force on the charged particles in the iron, moving charge is an electrical current, so there is a current flowing in the solid iron, possibly in the form of small local currents that are called eddy currents. Work is being done so the energy that originates in the magnetic step change is being dissipated as currents in the iron. I imagine this increases the rate of attenuation of the magnetic field over distance, but does it also change the velocity of the step change in the iron?

Ted

 

[Okefenokee]

EM fields can be expressed as a sum of waves (Fourier or Laplace transform). The time it takes for a field to propagate is always going to be related to the speed of a wave in the medium, in this case a transmission line made up of a rail road track. The speed of the waves is going to be determined by the composition and geometry of the transmission line and it will be frequency dependant.

You could write some differential equations for the transmission line then Laplace transform that. Next, calculate the Laplace transform of the input (probably a step function). Multiply those two thing then reverse Laplace transform it to get your result. You're pretty much guaranteed to get a time delay in your results plus some reshaping of the original input.

 

[Ted1]

thank you, so if I understand you correctly even though the force involved is magnetic and there is no electric field present, except self induction, the rules of EM fields apply, is that right?

The math you mention is way over my head unfortunately :-)

Can you say anything about how the situation might be different when the "rail" is changed from electrically conductive iron to electrically non-conductive ferrite, would it be correct to say that because there is no moving electric charge it follows there is no self-inductance and therefore no electric field? Would the step change in the magnetic field travel faster or slower in the non-conducting medium compared to the conducting one?

 

[ZapperZ]

thank you, so if I understand you correctly even though the force involved is magnetic and there is no electric field present, except self induction, the rules of EM fields apply, is that right?

This question is a bit strange because it seems to imply that you think that there are situations where it doesn't.

Magnetism, as in magnetic field, are part of our understanding of electromagnetic theory, as described by Maxwell equation. Now once you involve the material aspect of it, then the materials' property comes into play. Regardless of whether it is conducting or not, the value of the permeability of the material comes into play no matter what. Solving the wave equation tells you the speed of the light in that medium, and that corresponds to the upper limit of the speed of the magnetic field.

Zz.

 

[Okefenokee]

When electric fields change in time they cause a disturbance in the magnetic field. When magnetic fields change in time they cause a disturbance in the electric field. That happens with or without currents conducting.
No matter how you try to design your thought experiment the full set of Maxwell's equations will apply.

It isn't always necessary to consider the whole theory though. In your original thought experiment it would be a good enough approximation to say that the flux travels instantly. In a microchip where things switch in the GHz range, the speed of electricity becomes important.

 

[Ted1]

Zz thank you, about the implication, be clear, I am trying to learn the rules of electromagnetism, not challenge them :-) Thank you for mentioning permeability, I have to do some more studying to get permittivity (for insulators?) and permeability (for magnets?) straight in my head.

Okee, thank you for the approximation, I am trying to get a handle on how fast those magnetic domains in soft iron can realign under the influence of a step change. Thinking about the step moving up the rail, the domains are all in series, this one doesn't know to change until the one next to it has changed, and so on. And also isn't electron momentum involved, spin realignment? On the atomic and crystalline scales these seem to me to be dramatic events. For these effects to occur instantly would require infinitely large forces, and we don't have infinitely large forces here, or do we? Maybe I need to revise my understanding of the scale of magnetic energy? I think of a common bar magnet as something puny, but perhaps, on the atomic scale, it is enormously powerful, being capable of altering atomic structure, altering electron orbits for example. How should I view the energy in a common bar magnet? Puny or astronomical? Opinions welcome.

 

[Okefenokee]

Astronomical.

The individual charge carriers or magnetic moments might be small and move slowly but the fields they interatact with are powerful. I don't know much about material properties but I do know about fields. EM fields are far stronger than all the others. An interesting study is to calculate the gravitational attraction between two pennies on opposite sides of the globe then cacultuate the electric force if one penny was all electrons and the other was all protons. The difference is astounding.

You're doing good Ted. These are good questions.

Thinking about the step moving up the rail, the domains are all in series, this one doesn't know to change until the one next to it has changed, and so on.

The magnetic field stretches out forever in a continuous fashion. One domain has an effect on all domains in the universe, although it will be a small effect at great distances. One domain can affect much more than its imediate neighbors.

 

[Ted1]

thank you Okefenokee for the encouragement, I am still thinking about this. From Wikipedia I got information on permeability and permittivity that are helping me understand how the speed of an em wave is affected by the material, I haven't thought so hard about something in years :-)

I find it easy to believe an ordinary bar magnet is an unusual concentration of energy.