# Magnetic Energy

Q:
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
A:

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 energy, 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)

## Follow-Up #1: magnetic energy

Q:
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
A:

There’s energy 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 10/22/2007)

## Follow-Up #2: where does field energy come from?

Q:
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
A:

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 kinetic 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 10/22/2007)

## Follow-Up #3: Is force energy?

Q:
Hi you recentli answered that magnet do not spend any energi ... that is nonsence... if im take magnet and stick it to the iron plate on cealing its force will keep fighting gravyty ERGO it must do stronger oposite force and force is energi where is this energi coming from?
- Mitelin (age 28)
Czech
A:

Force is not energy. They aren't even quantities with the same units. Force is expressed as distance*mass/time2, while energy is distance2*mass/time2. That extra factor of distance in energy should serve as a reminder that work (transfer of mechanical energy) is done only when a force acts on something which moves some distance.

Mike W.

(published on 03/01/2014)

## Follow-Up #4: how permanent are magnets?

Q:
Hi there!I was searching for an answer to the same question as Sammy from Michigan, who started the thread. And yes, it seems you're missing what the problem is supposed to be, Mike W.Let me describe Sammy's and my problem this way:Suppose a permanent magnet is attached to the ceiling of a room. Now a steel plate is attached to this magnet. The magnetic force of the permanent magnet has to be stronger than the force of the gravity in order to keep the steel plate attached.Over time this permanent magnet must lose some of the energy used to magnetize it in production. One day the energy of the magnet is not enough anymore to sustain a magnetic force stronger than the gravity force of the steel plate. Thus the steel plate will fall down.Therefore, a "permanent magnet" is not "permanent", but must be depleting over time.This is our assumption based on the first law of thermodynamics.The funny thing is that you can't find much information about the "depletion" of "permanent magnets". Possibly this issue is so trivial to physicists that nobody publishes anything.Maybe you could post an equation for the "depletion" of "permanent magnets" or an equation showing the balance between input (magnetization) and output energy.Thanks in advance for your answers!L.
- Lucas (age 32)
Austria
A:

Yes, for ordinary-shaped magnets, the magnetized state has higher energy than states with much less magnetism. Those  lower energy states have a mixture of domains with magnetism pointing different directions. In the long run, the magnetic domains will rotate around toward one of the lower energy, less magnetized states. That isn't required at all by energy conservation (the First Law) but rather by entropy maximization (the Second Law).

That thermal demagnetization process can take an extremely long time. For example, geologists used magnetization patterns left in rocks for millions of years as a tool for studying their history. The typical time scales for the magnetization decay depend strongly on the type of magnetic material and the temperature, as well as other variables. So there's no simple equation.

For special shapes, e.g.  thin wires magnetized along the wire direction, the single-magnetic domain states are actually the ones with lowest energy. There are two such states, with the magnetic field pointing one way or the other along the wire. The time for thermal energy to randomly flip the magnet between these two states, at ordinary temperatures, can be longer than the age of the universe.

Mike W.

(published on 02/18/2015)

## Follow-Up #5: ways to lose magnetic energy

Q:
Hello,I have been helping my daughter with her school project and came across this conversation casually, and made me really interested and curious to follow up with few more questions.Q1: So, in the case of steel plate held to the ceiling by a magnet (let say a disk magnet), what is the expected timeline regarding magnetic field decay over time? is it in 10s, 100s, or more years?Q2: Suppose we have two permanent magnetic cylindrical discs in a non-conductive vertical tube - one is in a fixed position at the bottom of the tube, and the other one is positioned face to face to repel the fixed one. We force the moveable (floating) magnet down temporarily as close as possible to the fixed magnet and then release it (remove the force suddenly) for it to return to its equilibrium floating state. And we do this repeatedly. Assuming no contact friction with the inner tube surface. Where does the energy of the movement go? Is there any conversion to heat?Q3: If we coil a long wire around the same vertical tube and repeat the test above? 1) In one case the wire circuit is open (not connected to anything such as light bulb). 2) In the next case, we close the circut and connect to a light bulb or a volt meter and or an amp meter. What is expected to happen. Do we still have any heat generated in the process with case 1 or 2?Thanks,Cy
- Cy
Chicago, IL USA
A:

On your first question, about how long permanent magnets last, it depends on the material and the temperature. Refrigerator magnets are close to your description, and they stay stuck for many years.

With regard to the frictionless oscillating magnet, yes there will be gradual conversion of the energy to heat. Even if somehow contact friction is removed and even friction with air is removed, there's still a way for energy to get out. The oscillating magnet will radiate electromagnetic waves. Their energy will get absorbed somewhere, heating something up.

Coiling a wire in a closed circuit around the magnet will cause a much more rapid loss of energy. The current induced in the wire by the oscillating field will create heat in the circuit. If the circuit isn't closed, the wire won't matter much.

Mike W.

(published on 05/10/2015)

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