# Refrigerator Magnet Problem

1. Apr 24, 2006

### Ricardhheitman

I recently particpated in a thread that was closed out before I got the answer to what seemed to me a kind of paradox

A permanent magnet attaches to the side of a refrigerator. IT wont stay there forever , but it will for a very long time.

All that time gravity wants to pull the magnet off the side of the fridge.Somehow the magnet resists that.

1)Is energy being expended ?
2)If so what is the source
3) Can we calculate with any precision how much energy is needed to hold the magnet in place , or how much will be required to hold it in place for its useful life
4) When it finally does slide down after a long period of time, why does that happen? Because the energy to hold it in place has been used up , or because it is less magnetic than earlier in its life. If the latter , what changed it.

This discussion is interesting becasue the old thread raised a key question. Some people thought no energy was consumed because neither the magnet nor the fridge moved. Therefore no work , therefore according to the work function , no energy. Perhaps , but why does it stay in place for awhile but not forever ?

Others said the magnet was indeed exerting energy that was stored inside the magnet when it was created. I think what they would have said in more complete discourse is that when the substance the permanent magnet was made of was first magnetized , Energy in the form of a magnetic field caused individual iron molecules to arrange themselves into magnetic domains, and somewhatv like a spring being wound , the domains when they return from their aligned state to a different or unaligned state supply energy. So maybe the molecules in the fridge at the surface bond with the magnet have had their domains aligned with Fridge north to mag south etc. making the fridge a magnet uses up energy and eventually the magnets own alignment is lost , it is less magnetic , gravity wins and it slides to the floor.

So , any comments on either the questions or which of the two schools above were more correct?

2. Apr 25, 2006

### ZapperZ

Staff Emeritus
Start with a simpler scenario. You sit on a chair and you're not moving. Is energy being "expanded" here, as far as classical mechanics is concerned?

Zz.

3. Apr 25, 2006

### Ricardhheitman

Thank you Zapperz

I think I undertsand the work function. If nothing moves no energy has been expended.

But the force of gravity is pulling me to the floor all the time. If I dont sit in a chair but stick my rear out as if I was I am certain I am expending energy to keep from falling to the floor . I can feel it , and it can even be estimated calorically at the local fitness center.

The chair prevents me from falling to the floor and is exerting a force opposite that of gravity. In this case the strength of the wood or macromaterial and the energy that binds those molecules into fibers etc resists the force of gravity.

To me the differene here is someday the magnet will fall off. In your analysis it never will. Or are you saying that the potential energy I took out of the system when I placed the magnet on the fridge is somehow lost over time. If so , how would you describe what that process is

The other difference is the chair resists gravity due to the strength of the material at a macro level. The magnet refrig bond is electromagnetic force. Just doesnt seem an apt analogy.

And while I appreciate simple answers , why would not any chunk of metal not magetized also stick to the fridge? the same work is being done in terms of initial energy into the system.
What is it peculiar to systems with magnets that allows the work to be stored and fixed and useful to make things cling , attract etc

By the way I enjoy your Disney posts. Been too long since Ihave been there

Regards
Ricard

4. Apr 25, 2006

### ZapperZ

Staff Emeritus
It is why I emphasized the mechanics aspect of it.

You are confusing the definition of work, or energy expanded, as used in mechanics, versus the biological aspect of exerting your muscles and burning calories of your body. These two are not the same. In the physics of mechanics, how much your muscles expanded isn't usually taken into consideration when there's no displacement involved.

And just because something can affect something else, it also doesn't mean work is done. For example, a charge particle moving in a magnetic field. The magnetic force exerted on that particle is always perpendicular to the direction of motion of that particle. All the field does is to change the particle's direction without affecting its speed. It means that the field does NO WORK on the particle.

When you are sitting still on a chair, the NET FORCE on you is zero, or else you would be accelerating. So there are no energy expanded and no work done. That is the consideration based on kinematics alone.

Zz.

5. Apr 25, 2006

### Ricardhheitman

Thanks again

Hmmm. Would you say that if the direction of a particle with mass is altered by a magnetic field that no work has been done ?

In a way I have failed to make my question clear becasue you have not answered it . Why does the magnet fall off in time , and why doesnt any old chunk of matter become empowered to exert a lateral force perpendicular to that of gravity just by my hand holding it up there for a nanosecond ? Think of the applications in architecture if things just stayed in place once they were put there...

Also , and this does baffle me in your answer: The lectrons path is altered by the magnetic field. If we want electrons to move in a direction it is useful to have a magnetic field to guide them. But we have to put energy into creating the magnetic field so in order to achieve the result we have to do some work
There are equations to describe the exchange between the electron and the magnetic field that account for why the lectron will change direction. Are you saying those equations do not require any energetic interaction between the field and the mass less particle ?

6. Apr 25, 2006

### ZapperZ

Staff Emeritus
Not if the force is always perpendicular to the direction of the velocity, which is the case for the magnetic lorentz force.

Because the individual magnetic moment inside the material weakens over time due to thermal interactions, and interactions with other stray fields.

There's nothing wrong with doing work to produce magnetic field, yet it adds nothing to the system. I do this all the time here! However, the energy you created when into heat, and other forms of energy, including overcoming any self and mutual inductance of your coil. It isn't that transparent and simple.

Eh?

How did we get to "interaction between field and the mass less particle" all of the sudden?

Zz.

7. Apr 25, 2006

### Ricardhheitman

Sorry , I was attempting to have you explain what the nature of the interaction is between the electron and the magnetic field that will cause the electrons path to change.

I assume I can get the answer by learning what a " magnetic Lorentz force is and how it works on particles with or without mass.

But whether the force is perpendicular to the line of motion or not , if a particle with mass has its direction altered , work must have been performed according to law of motion

I will self study the Loerentz thing and maybe it will come clear.

It must be fun to be employed in this field

8. Apr 25, 2006

### ZapperZ

Staff Emeritus
What I'm telling you here isn't new, nor should be a surprise, if you look up in intro physics text. Work is defined as

$$W = \int{\vec{F} \cdot \vec{dr}}$$

It means that only a force with a displacement dr along the direction of the force F will have a non-zero dot product.

THIS, is the exact mathematical definition of work in physics.

Zz.

9. Apr 25, 2006

### Ricardhheitman

I understand the idea behind the force equation , I thank you for reposting it for me.

An electron is moving from right to left on this screen
<------------------------------------------------

The mganetic Loerentz force direction is from bottom to top of this screen

^
:
Force :
:

Which way will the direction of the lectron be altered? Pushed toward the upper left hand corner or pulled to the lower left hand corner

If the upper right doesnt that satisfy that there is motion or acceleration in the direction of force and therefore work is done ?

Substitute an ion of iron with a negative charge. Is the result the same

Substitute an asteroid made of iron whose surface layer is ionized by heat and the magnetic force in this case is very huge in aggregate.Still the same result and still no work ?

10. Apr 25, 2006

### ZapperZ

Staff Emeritus
I am not sure where you are getting your "information from". May I suggest you go to website such as the Hyperphysics site and learn about the magnetic Lorentz force law? I'm assuming you know what a cross product is.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html

You'll see that the magnetic force is ALWAYS perpendicular to the direction of v, and thus, the direction of the displacement.

Zz.

11. Apr 25, 2006

### Modey3

Ricardhheitman,

Here is the question you are trying to address: if a magnetic field does work, does the permanent magnet, which produces the field, expend energy?

First off, the magnetic field is created by the spin of the electrons in metal (since the motion of electrons creates a magnetic field). The spins of the electrons couple (or align themselves parallel to each other). This coupling keeps the coupled electron's spin aligned in the same direction.

In permanent magnets, all the electrons have their spins aligned (expect for a few random misalignments t=due to thermal excitations). To mis-align an electron against the alignment of the rest of the electrons takes work. You can apply a magnetic field against the polarization of the magnet that will cause the electrons spins to flip. This would require work. But in the case of a refrigerator magnet the work that causes the spins to flip is from thermal effects- not the field that the magnet produces. Theoretically, a permanent magnet at 0 deg K will produce a field that will never change. I hope this helps.

Regards
Modey3

12. Apr 25, 2006

### Ricardhheitman

Zapper

According to my interpretation of thsi in my diagram the lectron moves toward the upper left of the screen. Agree

Lorentz force
In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B. Combined they give the Lorentz force equation (or law):

where

F is the force (in newtons)
E is the electric field (in volts per meter)
B is the magnetic field (in webers per square meter, or equivalently, teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in meters per second)
and × is the cross product.
Thus a positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to the B field according to the right-hand rule.

13. Apr 25, 2006

### Ricardhheitman

Modey

many thanks for your post.

You are saying the magnet does not expend energy to stick to the fridge.The magnet recieved energy to align the spins of the material.
The atoms of the magnet once imparted with this spin will keep it forever in the absence of thermal or other random interactiosn that would input energy that will realign the spin of some of the electrons of some of the atoms in the magnet.

But what about the fridge? what energy was utilized to align atoms of the surface layer of the metal in the fridge opposite to the magnetic materials net moment so that they will attract and "stick togehter" with a bond stronger than gravity and friction in this example.

14. Apr 25, 2006

### ZapperZ

Staff Emeritus
No I don't, because you left out the direction of the magnetic field.

Note that as SOON as the direction of the velocity changes, SO DOES THE DIRECTION OF THE MAGNETIC FORCE! It will always be perpendicular to the motion of the charged particle throughout the trajectory! That's why you can get a charged particle in a circular motion, because you can get a perfectly central force! See a cyclotron!

Zz.

15. Apr 25, 2006

### Gokul43201

Staff Emeritus
This is the part that Richard is missing - that the direction of the force depends on the direction of velocity, and specifically is always, by nature of the Lorentz force, perpendicular to it.

16. Apr 25, 2006

### Ricardhheitman

Ah hah

So its like if a rocket engine were exerting a force against the direction of motion of an asteroid, but every nanosecond changing its own angle of attack to exactly be equal to the infintely small change in the direection of the asteroid accomplished by the thrust in the previous nanosecond

So we could move an asteroid without any work being performed. All of the energy applied in this system from the rocket engine would appear to be dissipated by heat.

A cool concept this change in direction without work.

The connection I am truely failing to make is how a permanent magnet sticks to a refrigerator without energy being utilized or work being performed. I stipluate there are systems that can accomplish important tasks without energy consumption or work ( see cyclotron) , but I dont really see the connection to the fridge magnet. Why does it stick , and is there a change in the composition of the electrons , spins domains or any other property of the fridge?

17. Apr 25, 2006

### Gokul43201

Staff Emeritus
It sticks because there is an upward force (which can not exceed a number proportional to the attractive force between the magnet and the fridge) that is as strong as the downward force (gravitational attraction from the earth).

Alternatively, I could answer, "For about the same reason that you stay stuck to the Earth instead of getting plucked off its surface (at noon) and flung into the Sun". However, no work is being done by the earth in keeping you happily on its surface.

18. Apr 25, 2006

### Modey3

Ricardhheitman,

You are actually asking a very involved question. If you want to know these sorts of details about magnents I can reccomend a few books for you. However, I'll do my best to answer your questions, and at the same time keep it under a page.

When you were a kid. Do you remember playing with those magnents that read "north" on one end and "south" on the other ? Imagine that the magnetic field created by the spins of the ELECTRONS in this magnetic material are represented by an array of these magnents. One spinning electron corresponds to one toy magnent For simplicity, consider a 10 X 10 array smaller (toy) magnents Do we agree that the magnent produces the highest field when all these smaller magnents are aligned? To answer your question about how does a magnetic material demagnetize....

It has NOTHING to do with the object it is attaching to (in the case the refrigerator). What causes a magnent to demagnitze is thermal fluctutations of the smaller magnents. Also, a internal field (the demagnitizing field) or an external field (from another weaker magnent) can speed up the process of demagnitization. But lets consider no other field except for the one that the magnent creates.

Initially every mini-magnet is aligned. THERMAL energy causes these mini-magnents to RANDOMLY FLIP with TIME. If one mini-magentns flips direction and the surrounding magnets have an opposite direction that mini-magnent will flip back cause is energetically unstable. If enough mini-magnents flip in a given area to form a cluster thats energetically stable they wont flip back to the original direction of the magnitization. Now it should be easy to see why a magnent demagnetizes. Yes, it involves energy: thermal energy.

Regards
Modey3

19. Apr 25, 2006

### Ricardhheitman

My thanks to both Gokul and Modey. It starts to become more clear.I do agree that the magnetic field is strongest when the alignment is perfect. I also concede enthusiastically that the process of demagnetization is thermal energy , and this makes sense becasue I know that magnetic substances are very sensitive to heat and cold.

Next I would like to know more about the attractive force exerted on the fridge by the magnet . A little iron bar of about the same length as the gap between the N and S poles of a permananet horseshoe magnet will cling most strongly when aligned directly across the gap. More to the point the magnetic field acts as if to move the little bar so that it rotates until it settles into this alignment.

I may have to draw this picture if I am not communicating clearly , but

1) Isnt the rotation of the little bar evidence that some energy is being expended to move it

2) Does the field act in any way to re arrange the structure of the target ( the fridge surface , the little metal bar) It seems to me it must because
in a plain steel bar that while susceptable to being magnetized isnt yet , the atoms with up and down net spin moments would be randomly distributed. It seems equally likely that the surface area directly "under" the north pole of the magnet would encounter positive net moment as negative , and the most likely is a net zero as the Ups and downs cancel each other out.

So for the sticky thing to happen the N pole must find some s poles in the target in enough concentration to allow a bond as strong as gravity .

So how does this happen ? How would the target material become aligned where under the N pole of the magnet is a concentration of S domains in the target. What force non randomizes the distribution ?
If any domain walls in the target are created , moved , made bigger or smaller , energy must be present.

OR

The nature of the bond requires no change in the target

Is it one or the other , both or some third thing?

20. Apr 26, 2006

### Modey3

Yes the energy of interaction between two magnents depends on the angle of their alignement. I'm not sure what level of math you have so I'm not going to go into dot product explaination. If two magnets are aligned parallel (meaning that the north and south ends are pointing in the same direction) those magnents are in their lowest state. If I offset the angle between these two magnents (I'm doing work on the magnetic field) those two magnents are at a higher energy and thus rotate towards each other thus LOSING energy (the field loses energy to the environment), but the energy of the magnentic material DOESNT change because the mini-magnents that represents the electrons spin still remain all aligned (if our thought experiment is done at 0 deg. K). You need to understand that a field can have its own energy INDEPENDENT of the energy of the material producing it.