What Causes the Magnet to Move When Its Field Reaches Iron?

[mrspeedybob]

For th sake of simplicity I will state the question in terms of magnetism but the same problem would arise from any of the 4 forces.

Suppose you have a self-contained electromagnet and piece of iron 300,000 kilometers apart. Each is at rest relative to the other and to the observer.

Switch the magnet on. 1 second later the magnetic field reaches the iron and applies a force to it. An observer can see it begin to accelerate toward the magnet. The magnet must begin to accelerate at the same instant or the center of mass of the two body system will move and violate the law of conservation of momentum. What causes the magnet to move when it's field reaches the iron? If the Iron were not there then the magnet would not move so it seems like the minimum reaction time of the magnet would be 1 second for the field to reach the iron and another 1 second for the irons effect on the field to be transmitted back to the magnet for a total of 2 seconds. As stated above though, this time lag would cause a violation of the law of conservation of momentum.

 

[tiny-tim]

hi mrspeedybob!

the electromagnetic field itself carries momentum

when the electricity is turned on, it "pushes" energy into the electromagnet, which converts it into both energy and momentum radiated outward

(the energy is the famous Poynting vector)

when the field reaches the iron, some of the momentum is lost from the field locally and gained by the iron

(of course, there'll be a small amount of "kick-back" propagated towards the electromagnet, but i should think it'll be pretty negligible by the time it gets there, 1 second later )

nobody every thinks of the poor old field, and how tired it's getting! ​

 

[mrspeedybob]

The momentum imparted by the magnetic field to the iron would be in the direction of the magnet, that would mean that the field is carrying momentum in the opposite direction of it's propagation. That seems weird to me.

Another thing that seems weird to me is that photons (the force carriers of electromagnetism) are mass-less so regardless of what momentum is transferred by the photons, the center of mass of the two body system is still defined by only the masses of the two bodies, the magnet and the iron. If the iron moves first I'm still stuck with a center of mass that moves.

I'm still not getting it.

 

[tiny-tim]

hi mrspeedybob!

Another thing that seems weird to me is that photons (the force carriers of electromagnetism) are mass-less so regardless of what momentum is transferred by the photons, the center of mass of the two body system is still defined by only the masses of the two bodies, the magnet and the iron. If the iron moves first I'm still stuck with a center of mass that moves.

(ignoring the question of whether these photons are actually real …)

no, a photon does have momentum, in fact its momentum is equal in magnitude to its energy (in a coordinate system in which c = 1)

The momentum imparted by the magnetic field to the iron would be in the direction of the magnet, that would mean that the field is carrying momentum in the opposite direction of it's propagation. That seems weird to me.

hmm … i see what you mean …

i've asked some other people for help on this point

 

[diazona]

Seems weird to me too. If one were to do a detailed calculation, I suppose the starting point would be Jefimenko's equations, which give the electric and magnetic fields produced by a given charge/current distribution, taking into account travel time between source and detector. I tried it myself but experience is showing there are quite a few little details that are easy to forget so hopefully someone will come up with a more intuitive explanation.

One other thing that I noticed: in relativity, the center of mass is not such a useful concept. You have to generalize it to the center of energy. So even though the iron moves before the magnet, it does not necessarily mean the center of energy moves, because you have to account for the energy stored in the EM field.

 

[MagnetDave]

Let's look at this from a material standpoint:

What does the iron DO when the field is applied? The material polarizes in response - it magnetizes as well. So the soft magnetic material turns into a magnet itself, with its own magnetic field that acts upon the magnet. This is your return field.

 

[JDługosz]

when the field reaches the iron, some of the momentum is lost from the field locally and gained by the iron

That's why magnetism can be shielded: something beyond the iron will feel a weaker force from the original magnet. This depletion shows up in the intercepted area as a weaker field?

(of course, there'll be a small amount of "kick-back" propagated towards the electromagnet, but i should think it'll be pretty negligible by the time it gets there, 1 second later )

Shouldn't it match, conserving momentum of the two bodies in the long term in a crude view, without looking at the fields?

 

[georgir]

Another thing that seems weird to me is that photons (the force carriers of electromagnetism) are mass-less so regardless of what momentum is transferred by the photons, the center of mass of the two body system is still defined by only the masses of the two bodies, the magnet and the iron. If the iron moves first I'm still stuck with a center of mass that moves.

Consider an even simpler example, an atom in space emitting a photon. The photon has a momentum in some direction, and the atom will gain an equal momentum in the opposite direction.

Photons don't have a rest mass, but they do have energy, and energy is equivalent to mass. You need to include that into your "center of mass" consideration.

As to your original question, yes it is quite interesting. Unfortunately we can not translate it for other kinds of forces, as we aren't able to arbitrarily switch them on/off.
I must confess I can't at all understand magnetism in terms of photon-matter interactions, so I'll skip commenting on that for now. I only want to note one thing about the assumption that the iron and the magnet should start to move "simultaneously" - simultaneity is in fact dependent on the reference frame, so this assumption can not always hold.