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This is a follow-up question to my Physics SE question from yesterday:

How is magnetic energy supplied?

The kind responses were very informative, but I still have much to understand about magnetism, as follows:

Scenario:

Imagine a piece of iron laying on an infinitely large flat surface. A magnet is also positioned on the surface, some distance from the iron. The iron is thus attracted to the magnet and slides sideways across the surface. As the iron moves, the magnet is moved in tandem with it such that the iron is never allowed to contact the magnet. Thus, the sliding iron is forever "chasing" the magnet across the surface.

Question:

Friction from the iron sliding across the surface results in dissipated heat and sound energy. Since energy can never be created nor destroyed, I presume that the heat and sound energy is derived somehow from the magnet. What then, is the source of that energy, and how is it constantly supplied to the magnet?

Stu Smith
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    Who’s pulling the magnet? – Bob Jacobsen Jul 17 '19 at 15:54
  • Bob has already pointed out that here, the source of energy is the person pulling the magnet. But you might ask about the alternate scenario where no one is pulling the magnet and the iron and magnet end up touching each other. There was still some energy that came from somewhere; in this case it comes from the magnetic field itself. – sasquires Jul 17 '19 at 16:16
  • @Bob Jacobsen Well, I'd take a try at it, but would probably eventually get bored and wander off for a pint. So I suppose some sort of mechanical contrivance would make sense. Maybe instead of an infinitely large surface, the iron-magnet "pair" could travel on some sort of moving belt or treadmill. – Stu Smith Jul 17 '19 at 16:17
  • There are a lot of other questions that you could ask about how magnetic fields supply energy and how that is consistent with the Lorentz force and the work-energy theorem. This has been discussed before, e.g., here. – sasquires Jul 17 '19 at 16:17
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    Then whatever is powering the belt or treadmill is supplying the energy. – sasquires Jul 17 '19 at 16:18
  • @sasquires In your first comment where the iron and magnet end up touching, the energy (by that I assume you mean the heat from the clicking noise when they touch) "... comes from the magnetic field itself." That implies a resulting energy deficit in the magnetic field. So how and from where is that deficit replaced? – Stu Smith Jul 17 '19 at 17:07
  • @sasquires your comment that "... whatever is powering the belt ... is supplying the energy." is interesting! If I understand correctly, the iron is drawn to the magnetic potential "well" (did I say that correctly?), and thus will continue to move as that well itself moves. But I still can't visualize the energy "flow" from the movement of the magnet to the frictional heating. – Stu Smith Jul 17 '19 at 17:13
  • The "energy deficit" in the magnetic field works the same way as it does for gravity. The example of gravity is much more intutive for most people. Suppose that you come to my house and find me holding a book in the air at face height. Then I let go. Where did the energy come from? It came from the gravitational field that surrounds the earth. Afterwards, there is a sense in which this field (or, if you prefer, the gravitational system involving the earth and other nearby massive objects) has less energy. If I lift the book up again, the original state will be restored. – sasquires Jul 17 '19 at 17:41
  • In your scenario: The iron would lose energy via friction, but it also gains energy by being pulled on by the magnet. By Newton's third law, the iron also pulls on the magnet and slows it down, so it would lose energy, but it is being pulled by the conveyor belt, so it doesn't. Again by Newton's third law, the magnet pulls the belt and would slow it down, except that it is being powered by an external motor. So the net result is that heat is being deposited in the surface and the motor is expending energy, but the "energy levels" of everything else is constant. – sasquires Jul 17 '19 at 17:49

1 Answers1

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That implies a resulting energy deficit in the magnetic field

I think all of your questions ultimately boil down to some variation of this statement.

So...

The problem is that you're ignoring everything before and after "the event". You're creating an artificial line around the system, both physically and in time, and noticing there's a change in energy inside that line and wondering what is going on.

But if you simply expand the line a little the mystery will go away. For instance, you have noted that when the iron bar moves to the magnet (in the static case, no belt), it gave off heat due to friction. So that must imply that the magnet has lost energy somewhere?

No. Simply placing the iron on the sheet required energy. It required energy to keep it away from the magnet in the first place. Think about it - if the magnet is strong enough to pull the iron bar when it's sitting on the surface, then it's strong enough to pull it when it's in your hand before putting it on the surface. So you had to expend energy to keep it away from the magnet when you put it down. That's the energy that ultimately came out as heat (and sound).

So when you see a potential paradox or missing energy, ask yourself "how did we get here in the first place?" - move the line you're drawn around the experiment and see what suddenly appears. For instance...

There is a ball at the top of a hill. It rolls down the hill and hits a box. That gives off heat. Did that energy come from gravity?

No, the energy came from you walking up to the top of the hill to put the ball there in the first place.

This is going to be true of all "conservative" forces, like gravity or magnetism (or lots of others).

Maury Markowitz
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  • Many thanks to all who added to my knowledge about magnetism. As a botanist, I tend to visualize energy "flowing", as in: solar fusion begets electromagnetic waves/particles, which beget chemical bonds via photosynthesis, which beget my respiration (via that pint!). To someone unfamiliar with that "flow", it would all seem somewhat mysterious, just as magnetism is mysterious to me (although less so, thanks to SE!). Comparing magnetism to gravity helped me greatly because we constantly live in a world where gravity is manifest, magnetism less so. – Stu Smith Jul 18 '19 at 16:45