What Powers the Attraction Between Two Permanent Magnets?

[MisterBig]

I place two permanent magnets on a desk so that their poles are orientated for attraction. I take my hands away and they move towards each other. Where does the energy come from? Are the magnets now slightly less magnetic?

 

[sridhar_n]

...

The energy comes from the potential energy stored in the field.


Sridhar

 

[MisterBig]

Originally posted by sridhar_n
The energy comes from the potential energy stored in the field.

So are the magnets now slightly less magnetic?

 

[sridhar_n]

No they are not less magnetic...The Total energy is always conserved.

Sridhar

 

[chroot]

It is true that two magnets stuck together weigh ever so slightly less than two magnets pulled apart. The energy difference affects the mass (as per relativity theory). In day-to-day experience, energies are much smaller than masses, so the effect is rather difficult to demonstrate -- except in nuclear reactions.

- Warren

 

[HallsofIvy]

C'mon chroot. That true but irrelevant to the question!

Mr. Big: how did the two magnets get into the intial position?

It is easy to see that if the two magnets were in position next to one another and you separated them a distance d, then the work done is exactly equal to the potential energy of one relative to the other and equal to the kinetic energy that one gains moving toward the other.

It is pehaps harder to see but still true that if the two magnets were created (dug out of lodestone perhaps!) a large distance apart and then moved to the position closer together, you still would have to calculate their initial potential energy, reducing it if necessary as they were moved into position, you still have some potential energy- equal to whatever work was done to create the two magnets and then move them into position. That potential energy is equal to the kinetic energy increase as they move together (minus any work done by friction to slow them).

 

[chroot]

Originally posted by HallsofIvy
C'mon chroot. That true but irrelevant to the question!

Uh, no it's not. When the two magnets are close, they are more massive. Thus, the react less strongly to the magnetic field, per Newton's second law. This seems to answer MisterBig's question.

MisterBig was confused because he didn't understand where the potential energy went when he let go of the magnets and they snapped together. The answer is: mass.

- Warren

 

[lethe]

Originally posted by chroot
Uh, no it's not. When the two magnets are close, they are more massive. Thus, the react less strongly to the magnetic field, per Newton's second law. This seems to answer MisterBig's question.

being more massive does make the magnets accelerate more slowly, but it does not affect how magnetic they are, which is an intrinsic property of the metal. it doesn t change how strong the force they exert on each other it.

i think this is why Halls said your comment is irrelevant

MisterBig was confused because he didn't understand where the potential energy went when he let go of the magnets and they snapped together. The answer is: mass.

- Warren

that is not the answer. the answer is that the energy changed from the field to kinetic energy.

when you change some energy from electromagnetic potential energy, to some other form of energy, the total mass of the system does not change. this is a statement of the conservation of mass energy.

what does happen is that some of the energy leaves the field, and goes into kinetic energy of the magnets.

that is where the energy goes then. if you account for the increased temperature of the magnets or wherever their kinetic energy ends up, you will find that the total mass of the system does not change, as it cannot for any closed system.

for the mass of the system to change, energy must leave the system.

 

[chroot]

Originally posted by lethe
for the mass of the system to change, energy must leave the system.

Hmm.. now I'm getting confused.

If you bring the magnets together very slowly, so their kinetic energy is negligible, then you have two states:

initial state: magnets separated, higher mass

final state: magnets together, lower mass

Since you're bringing them together slowly, there's no "bang" at the end when they touch, so there's neglibible energy lost to heat or sound. Am I correct that in the limit as the magnets are moved together at zero velocity, there is no energy lost?

- Warren

 

[lethe]

Originally posted by chroot

Since you're bringing them together slowly, there's no "bang" at the end when they touch, so there's neglibible energy lost to heat or sound. Am I correct that in the limit as the magnets are moved together at zero velocity, there is no energy lost?

well this is a little complicated by the fact that we have magnetic dipoles instead of say, statically charged objects.

in the electrostatic case, it is clear, it doesn t matter how slowly you move, the energy released must go into kinetic energy. this is a direct consequence of the fact that the electrostatic force is conservative.

so if you have two opposite charges, with some separation so there is a potential energy, then there is some rest mass in the charges, and some mass in the field. then you move the charges together, slowly or quickly, makes no difference, and the energy is released from the field.

if you send this energy away, then the mass of the total system decreases (just like when two protons combine to make helium and lose the extra energy by radiation, the mass decreases)

on the other hand, i don t really care about whether the mass decreases. i have already answered the question of where the energy came from: it came from the field. now if i do want to know about the mass of the system (whether it decreases or not), then i have to specify what happens to the extra energy. it could be radiated away, in which case mass decreases. or, i could attach some springs, and convert electromagnetic potential energy into spring potential energy, and then the mass will stay the same (since no energy has left the system). it could turn into thermal energy, and then mass will be the same if i count the surroundings, but not otherwise.

the point of the story is, it is irrelevant where the energy goes after it is released from the field. the question on the table is where the energy came from: it came from the field.

so whether the mass of the system increases or decreases is irrelevant.

 

[joshi-wan kenobi]

Does that mean if you pull the magnets apart and then bring them back together over and over you're charging the fields, then using the energy when you let them attract every time? Sorta like a kenetic-to-magnetic battery?

 

[MisterBig]

Separating the magnets and letting them slam back together again makes sense to me. It’s when you allow the magnets to join and then separate them that bothers me. It seems a bit like cause preceding effect - the kinetic energy is released and then I provide the energy used in that release by separating the magnets.

I think this is part of an ongoing problem i have with potential energy. At what distance is the potential energy between the 2 magnets at its maximum?

 

[lethe]

Originally posted by MisterBig
Separating the magnets and letting them slam back together again makes sense to me. It’s when you allow the magnets to join and then separate them that bothers me. It seems a bit like cause preceding effect - the kinetic energy is released and then I provide the energy used in that release by separating the magnets.

normally, you have to provide new energy to separate the magnets again, since the energy released when they combine turned into thermal energy, which you cannot regain. however, if you set it up right, you can catch this energy (like if you put an ideal spring between the two magnets).

I think this is part of an ongoing problem i have with potential energy. At what distance is the potential energy between the 2 magnets at its maximum?

the maximum of potential energy occurs when the separation is infinite.

 

[MisterBig]

Originally posted by lethe
the maximum of potential energy occurs when the separation is infinite.

Does this mean that every magnetic body in the universe has (near maximum) MPE in relation to every other magnet in the universe. Thats a lot of MPE, where does it keep it all?!

 

[HallsofIvy]

"near maximum mpe" doesn't make sense. Potential energy is always relative to some arbitrary reference.

 

[russ_watters]

Originally posted by chroot

Since you're bringing them together slowly, there's no "bang" at the end when they touch, so there's neglibible energy lost to heat or sound. Am I correct that in the limit as the magnets are moved together at zero velocity, there is no energy lost?

- Warren

How do you bring them closer without expending some energy in another way? Friction? Springs? There's energy there.

Its one of those trick questions of mechanics, I think - it makes you forget that there is other energy involved.

 

[MisterBig]

Originally posted by HallsofIvy
"near maximum mpe" doesn't make sense. Potential energy is always relative to some arbitrary reference.

My reference point would be any magnetic body.

I am holding a magnet does it "contain" MPE in relation to all other magnetic bodies?

 

[canadmonster]

No they are not less magnetic...The Total energy is always conserved.

Sridhar

so in a magnetic motor the magnetism will never be lost?

 

[canadmonster]

 

[mgb_phys]

Perpetual motion machines don't work.
The trick here is to have a compressed air jet just out of shot pointing at the edge of the pie tin or a battery and some hidden wires to the motor.