Q & A: magnetic energy

The law of conservation of energy says energy can’t be created or destroyed. So what’s the deal with permanent magnets? They spend energy attacting ferrous materials. Where does the energy come from that resupplies what was spent to attract?
- Sammy
Michigan

Why do you say that magnets 'spend energy' attracting magnetic materials. If the material is attracted to the magnet and moves closer to it, the magnetic potential energy goes down. That's just like when something falls toward the Earth and the gravitational potential energy goes down. Now if the object is stopped somehow (say by friction) that energy turns into thermal eenrgy, just like when a ball gradually stops bouncing.

If something (e.g. you) then pulls the object away from the magnet, then that's what supplies some more energy to the system- the same as how you have to supply energy to lift something up in a gravitational field.

I guess I'm missing what the problem is supposed to be.

Mike W.

(published on 10/22/2007)

To elaborate on the question then:

Imagine one takes a permanent magnet and a golf ball. One lays down the magnet on a flat surface and 1 inch away lays down the golf ball on the same surface. No more energy is added or removed from the system. The magnet and golf ball remain 1 inch apart.

Now repeat the procedure with the same magnet and a steel ball bearing rather than a golf ball. No additional energy is added to the the system yet energy is expended by means when the magnetic field around the magnet attracts the ball bearing, rolling it across the flat surface. From where did this energy come?
- Dave Cline (age 45)
Lake Oswego, OR

There’s enregy in the magnetic field in either case.  With the steel ball, the system has a way to reduce that field energy by having the ball approach the magnet. A lot of the energy goes into kinetic energy of the ball.  For the golf ball, all the field energy just stays in the initial form.

Mike W.

(published on 08/16/06)

What about a thought experiment where you introduce the steel ball at a very far distance and sideways to the field lines so almost no force is exerted against the field. Then the ball is released and moves towards the magnet. How many balls could be introduced this way before the energy in the magnetic field is all used up?
I guess what I’m really asking is this: unlike a rubber band which only has potential energy when it’s stretched, there is intrinsic energy in the magnetic field before we
do anything to it. Where did it come from? Doesn’t it tell us something about the way the universe was made? I suppose the same questions could be asked about gravity.
- Gayle (age 46)
Amarillo, TX

Great question. I'll skip the warmup and go right to your key point: where does the field energy come from?
Typical permanent magnets are made deliberately. Some magnetic material is heated up, a magnetic field applied, and then the material cools in the field. Lots of energy is wasted in this process, but let's follow just where the field energy is made. Initially the material has magnetic domains pointing in every direction, so their fields approximately cancel, leaving essentially no field energy outside the magnet. When a field is applied (usually via an electromagnet) to the warm material, it lines up the domains. It takes energy input to that electromagnet to do work lining up the magnetic domains. So the energy came from whatever supplied the electrical power.

Yes, the same sort of question could be asked about gravity or any field. Tracing the various energies in the universe back to shortly after the Big Bang, I guess you'd say that the big forms of energy then were the rest mass (energy) of particles (many of which then decayed) and the inetic energy of their relative motions, There are other ways of expressing and thinking about those energies, e.g. as field energies, however. As for how it all got started in some state, nobody knows. (Admittedly that's pretty much a non-answer.)

On your other question, you can tell when a lot of the field energy is gone because that's the same as when the field is much weaker. You'd notice that the next ball was not pulled in very much.

Mike W.

The total energy in the system also depends on the configuration of the balls.  The energy in the field is directly proportional to the integral of the square of the field strength over the whole volume, plus terms from the interaction with the material.  If you can arrange the balls to divert field lines farter away from the magnet and cause them to take longer paths around, then you have increased the energy of the system.  An example of this -- a bar magnet with a bunch of iron balls will likely have its lowest energy content when a chain of balls lines up from one pole to the other, allowing the fringe field of the magnet to follow the chain of balls, reducing the field outside the region containing magnets and balls.  If you move the balls around, say stack them up end to end all on the North pole of the bar magnet, then the energy of that configuration will be higher than the one I described above.  You'd have to hold the balls in place with some other force, or they will eventually end up in their lower-energy configuration.

  Some actions involve repulsive forces, where to bring in an an additional magnet, you must add energy.

  Tom

(published on 08/21/06)