# B Where do magnets get their energy?

1. Nov 24, 2016

### Jimmy87

It seems like magnets have an enormous supply of energy. Where does a magnets energy come from? It almost seems like it has a never ending supply of it.

Think of this thought experiment. A permanent magnet is suspended 1m away from the floor. A steel ball is placed onto the floor under the magnet - so its 1m away from the magnet. Let's say that the steel ball has a mass of 1kg. Let's also say that when it is placed onto the floor the magnet is strong enough to attract the ball all the way up to the magnet. Energy transferred by the magnet is work done which is force x distance and in this case it would be: weight x distance which is equal to 1J. So the magnet performed 1J of work. Let's say I repeat this experiment an infinite number of times (maybe that's a bit too much but you get the idea). Where does all this energy come from? Will it reach a certain number of steel balls before it can no longer do any more work? Thanks.

2. Nov 24, 2016

### Bystander

How much energy do you put back pulling the object away from the magnet?

3. Nov 24, 2016

### Staff: Mentor

Yes. The energy density is proportional to B^2. Each ball reduces the field. When there is not enough energy left then the field cannot lift any more balls.

4. Nov 24, 2016

### Jimmy87

I see your point. If the magnet does 1J of work where does this come from exactly and when you move it away where does it get put back? Also, suppose I use an infinite number of steel balls, i.e. different ones each time so I don't take them back away?

5. Nov 24, 2016

### Bystander

Then @Dale 's observation applies.

6. Nov 24, 2016

### Jimmy87

That's answered the second part of my question, thanks. Where does this energy density come from exactly when the magnet is made? Also, as the magnet's energy density decreases what is happening to the magnet? Is it that the domains start to misalign?

7. Nov 24, 2016

### Bystander

8. Nov 24, 2016

### Staff: Mentor

It isn't what is happening to the magnet. It is what is happening to the field. The ball get magnetized, and its field reduces the magnet's field.

9. Nov 24, 2016

### Jimmy87

So if we go back to the one ball situation. If you released it from one metre then pulled it back to one metre and kept repeating this would the energy density remain unchanged?

10. Nov 24, 2016

### Staff: Mentor

Yes, neglecting any hysteresis or damage to the magnet.

11. Nov 24, 2016

### Jimmy87

Thanks. So from your comment before are you saying that each ball that is sticking to magnet is applying a field that opposes some of the magnet's field and as you add more and more balls you are cancelling more and more of the field and as you move them back away the field lines get restored? Or have I misunderstood?

12. Nov 24, 2016

### Staff: Mentor

Yes, that is correct.

13. Nov 24, 2016

### RealBrokerCam

Are you suggesting that there is a definite amount of magnetic energy in existence?

14. Nov 24, 2016

I think @Bystander has it correct (post #2) in that it takes quite a large amount of energy to pull them apart. There are basically two types of magnetized material: 1) A good permanent magnet like the one that is put at the upper position that lifts everything and 2) A piece of soft iron that can become magnetized upon being placed in a magnetic field, and that becomes demagnetized once the field is removed. $\\$ I think this experiment can be performed quite repeatedly. I don't think a high quality permanent magnet loses its magnetization throughout its use. An example of this is the permanent magnets in electric motors. They can last nearly indefinitely. With their high Curie temperature (750 degrees Centigrade and higher), high quality permanent magnets are extremely stable and their permanent (nearly permanent) magnetization is unaffected unless they encounter very strong magnetic fields in the opposite direction or extremely high temperatures. $\\$ editing... I think the magnetized state, particularly in the case of a permanent magnet is actually lower in energy than the unmagnetized state, and that is why the magnetized state is such a stable one. $\\$ Additional item: For two magnets that are attracting each other, their fields (the B field) are aligned and the magnetic field inside of each of the magnets is actually stronger than without the field of the other adding to it.

Last edited: Nov 24, 2016
15. Nov 24, 2016

A follow on: A similar experiment could be performed with charged particles or charged objects containing opposite charges. As long as the electric charge doesn't escape from the surface, the capacity for the charged object to attract the other does not change. Again as @Bystander has pointed out, it will still require some substantial (and conserved) amount of energy to separate the objects.

16. Nov 24, 2016

### Staff: Mentor

If you knew the B field throughout all space then you would also know the amount of magnetic energy throughout all space.

17. Nov 24, 2016

@Dale You are forgetting the energy of the magnetization $M$ in the magnetic field: Energy per unit volume $U=-M \cdot B$. This also needs to be considered when determining whether the formation of a permanent magnet is energetically favorable. e.g. paramagnetic materials do not make permanent magnets because the magnetization $M$ is insufficient.

18. Nov 24, 2016

### Staff: Mentor

Yes, if you are using the macroscopic formulation then you need to include M. If you are using the microscopic formulation then you only need B.

19. Nov 24, 2016

A google of the topic "the magnetic energy of a permanent magnet" gave what I think are some very incomplete answers. (e.g. a website from the U of Illinois at Urbana and a couple others.) It would be nice to find a good authoritative source on the topic. I am going to try googling it a second time... I have actually done some back-of the-envelope calculations on the energy that give a requirement that $\chi'>(1/(4 \pi))$ ( c.g.s. ) units for the formation of a permanent magnet where $M=\chi' B$, but I haven't seen any books or papers that do a similar calculation. This is in agreement with another method I have of calculating it, but the permanent magnet topic doesn't seem to have gotten much attention in the E&M textbooks.