Does magnetic field do any work

[kanato]

That's true, but we don't have to consider the nail hitting the magnet. Consider the initial system to be the magnet and nail before the nail begins to move, and the final system to be the magnet and nail where the nail has picked up some kinetic energy. In this case I can set the final time to be well enough before the collision that the internal quantum systems of the two systems are isolated enough from each other to be independent, and the only interaction between them is through a classical B field.

How can these two sysyems be isolated frome ach other if they interact electromagnetically and exchange energy?

I meant that they are far enough apart that the quantum state of one system doesn't affect the other, except through the classical B field that is generated.

In this case, the internal free energy of the magnet can't decrease; it's already at its lowest value. (I suppose there may be some feedback from the B field caused by spins aligning in the iron nail, but I would imagine that's small compared to the other energy scales in the problem, because the nail doesn't pick up the same magnetization as the magnet.) The iron nail has picked up classical kinetic energy, and the only place that could really come from is from the breakdown of domain walls in the unmangetized iron allowing it to form a net magnetic moment.

But the energy will decrease later, so it can not be at its lowest value

What energy will decrease later? The total energy? But below you say it's conserved?

I'm dividing the system up into several energy systems:
E_{int}^{mag} + E_{int}^{nail} + T_{nail} = \mathrm{const}

where E_{int} is the internal energy of the magnet or the nail, determined by the quantum mechanical structure of the material, and T is the macroscopic kinetic energy of the nail. The total energy is conserved. My argument was that E_{int}^{mag} is already at its minimum value due to its Ferromagnetic order, but E_{int}^{nail} can go down if the spins within the nail align. This allows the kinetic energy to increase.

The bottom line is that the total energy of a closed system is always conserved. There are however no truly closed system because of radiation and similar stuff. So you need to consider the initial energy (before the motion started) and the final energy (after the collision and everything settling down). Obviously, the second will be less that the first and the difference will be carried away by radiation to infinity.

You don't have to consider the final state to be after the collision. You can if you want, but energy is conserved <i>at all times</i> so I can pick any initial and final times that I want.

When the magnets attract each other, there is an increase in kinetic energy. I'm interested in understanding when where that energy comes from. Once they collide, yes that kinetic energy goes somewhere (thermal energy, perhaps into disordering the spins too) but I don't care about that; it's not fundamentally different from any other collision.

Another aspect is the following: you can write a Lagrangian and a Hamiltonian of a system of moving charges only to the order \beta^2, where \beta=v/c. This is significant because radiation is an effect which is third order in \beta. That means that in our energy balance analysis we can only consider the initial and final states of the system when the is no motion and no radiation.

Can you elaborate on this? The expansion comes from expanding \gamma = (1-\beta^2)^{-1/2} in a Taylor series, right? This can be carried out to arbitrary order right? What barrier is there to preventing doing this in the Lagrangian formalism?

Are you talking about radiation from accelerating charges? Because IIRC the radiation for positive and negative charges has a pi phase shift, so accelerating a neutral system (like the iron nail) doesn't cause a significant amount of radiation because of destructive interference of the waves.

 

[burashka]

I meant that they are far enough apart that the quantum state of one system doesn't affect the other, except through the classical B field that is generated.



What energy will decrease later? The total energy? But below you say it's conserved?

I'm dividing the system up into several energy systems:
E_{int}^{mag} + E_{int}^{nail} + T_{nail} = \mathrm{const}

where E_{int} is the internal energy of the magnet or the nail, determined by the quantum mechanical structure of the material, and T is the macroscopic kinetic energy of the nail. The total energy is conserved. My argument was that E_{int}^{mag} is already at its minimum value due to its Ferromagnetic order, but E_{int}^{nail} can go down if the spins within the nail align. This allows the kinetic energy to increase.



You don't have to consider the final state to be after the collision. You can if you want, but energy is conserved <i>at all times</i> so I can pick any initial and final times that I want.

When the magnets attract each other, there is an increase in kinetic energy. I'm interested in understanding when where that energy comes from. Once they collide, yes that kinetic energy goes somewhere (thermal energy, perhaps into disordering the spins too) but I don't care about that; it's not fundamentally different from any other collision.



Can you elaborate on this? The expansion comes from expanding \gamma = (1-\beta^2)^{-1/2} in a Taylor series, right? This can be carried out to arbitrary order right? What barrier is there to preventing doing this in the Lagrangian formalism?

Well, assume you have a system of N classical charged particles. You then want to write a Lagrangian for this system. In the zeroth approximation

L = \sum_i m_iv_i^2/2 - \sum_{i&gt;j} q_i q_j /r_{ij}

But this completely neglects retardation.
At the next step, we can try to write the lagrange function for every particle in a given field and then compute that field as a function of all particle positions. We have

L_i = -mc^2\sqrt{1 - v_i^2/c^2} - q_i\varphi + (q_i/c){\bf A} \cdot {\bf v}_i

Here \varphi,{\bf A}[\tex] are the scalar and vector potentials. It is not difficult to see that if we do not make any approximations, the resultant sum of all L_i is not the proper Largange function of the system. In particular, it would not result in proper energy conservation laws. This is explained by the fact that the field in electromagnetic theory itself has a number of independent &quot;degrees of freedom&quot; which must be included into the Lagrangian. Only then the total energy is conserved. <br /> <br /> It is possible, however, to expand the Lagrangian to the second order in v_i/c[\tex]. This amounts to neglecting radiation. &lt;br /&gt; &lt;br /&gt; &lt;br /&gt; Are you talking about radiation from accelerating charges? Because IIRC the radiation for positive and negative charges has a pi phase shift, so accelerating a neutral system (like the iron nail) doesn&amp;#039;t cause a significant amount of radiation because of destructive interference of the waves.

&lt;br /&gt; &lt;br /&gt; A truly neutral system of course can not radiate. But the magnetized object, when moves through space, would create time-varying fields and this leads to radiation. You can not view a magnetized object as electrically neutral. It has currents running in it and these currents are made of charged particles.

 

[burashka]

I meant that they are far enough apart that the quantum state of one system doesn't affect the other, except through the classical B field that is generated.

But you can not through this interaction away since it is important. So the magnet and the nail are not isolated. When you assume that they are, you neglect the very effect you want to consider.

What energy will decrease later? The total energy? But below you say it's conserved?

Yes, the total energy is conserved, including the energy of radiation that will eventually go to infinity. The energy of the atoms that make up the magnet and the nails will be decreased.
Or do you suppose that a system can never go from an excited state to a ground state because the total energy must be conserved?

 

[burashka]

You don't have to consider the final state to be after the collision. You can if you want, but energy is conserved <i>at all times</i> so I can pick any initial and final times that I want.

When the magnets attract each other, there is an increase in kinetic energy. I'm interested in understanding when where that energy comes from. Once they collide, yes that kinetic energy goes somewhere (thermal energy, perhaps into disordering the spins too) but I don't care about that; it's not fundamentally different from any other collision.

I am not sure I understand. The energy doesn't have to come from "somewhere". It is simply conserved at all moments in time. But you have to account for all energy, including the energy of EM fields. In the example of a magnet and a nail, the magnet makes an H field around itself and that field has energy (and also mass according to E=mc^2). When the nail starts moving, it acquires some kinetic energy but the EM fields arond the objects also change and the total energy is conserved. It is however, not easy to see in detail how this happens. So it is better to consider the end-points, when everything is static.

 

[kanato]

I am not sure I understand. The energy doesn't have to come from "somewhere". It is simply conserved at all moments in time.

The kinetic energy has to come from "somewhere." In order for the kinetic energy of the iron to go up, the energy of some other subsystem has to go down. That's what conservation of energy means. That's what I'm saying I want to understand, what other energy subsystem goes down? I don't understand how is this not clear to you.

But you have to account for all energy, including the energy of EM fields. In the example of a magnet and a nail, the magnet makes an H field around itself and that field has energy (and also mass according to E=mc^2). When the nail starts moving, it acquires some kinetic energy but the EM fields arond the objects also change and the total energy is conserved. It is however, not easy to see in detail how this happens. So it is better to consider the end-points, when everything is static.

You don't have to account for all the energy, only the energy subsystems that change significantly. I have a very hard time believing that there is significant radiation moving the weakly magnetized iron. The speeds here are such that v <<<< c, so any effect that is \beta^3 should be quite negligible. So I'm assuming that it's negligible.

That lagrangian you wrote down is not the related to the system I'm describing. You have charges in there, but there is nothing charged here. The magnet and the iron are both neutral.

 

[HarleySpirit]

To simplify:
http://en.wikipedia.org/wiki/dirac_bracket

Wikipedia makes magnetic force a little clearer. Dirac bracket is a bit more direct than your explanation.

 

[burashka]

That lagrangian you wrote down is not the related to the system I'm describing. You have charges in there, but there is nothing charged here. The magnet and the iron are both neutral.[/QUOTE]

Any macroscopic object is made up of electrons, protons ane neutrons. Except for neutrons, these are charged particles. And if the object is magnetized, they surely move around with relativistic velocities. As you must know, magnetization is a relativistic effect. That's why it is usually so week.

Well, it is not so week if it is caused by spins. But spins themselves are relativistic and can be only understood properly from the Dirack equation.

And yes, the energy is in the field. When a system of charged particles move, the energy of the particles + the field must be conserved.

When you turn on a lignt bulb, where do you think those 100Watts go?

Same with magnetism.

 

[HarleySpirit]

Monopoles to dipoles simplified

GUT advocates, please don't give me *that* look: perhaps we have a simpler explanation for monopole/dipole conversion than Dirac and Hawking allow:

Rip apart a proton and we see UUD quarks. Couple UD and we have a -1/3 monopole. Couple DD and we have a -4/3 monopole. Etc.

Free leptons also present as monopoles in lower dimensions Su/SUn>1d.

Your thoughts?

 

[HarleySpirit]

That lagrangian you wrote down is not the related to the system I'm describing. You have charges in there, but there is nothing charged here. The magnet and the iron are both neutral.

Note that we're talking fields. EM fields are stronger than gravity here, depending on temperature. Note also that EM fields have strange effects on superconductors.

Why?

Magnetic domains like to stay aligned until we heat the magnet, disordering the domains. When we just heat the field, we see a concurrent increase in the field (Curie's Second Law).

Any macroscopic object is made up of electrons, protons ane neutrons. Except for neutrons, these are charged particles. And if the object is magnetized, they surely move around with relativistic velocities. As you must know, magnetization is a relativistic effect. That's why it is usually so week. [Sp: weak]

Observe conservation of energy: add energy to a field, the field strength increases: E=2/pi\RT.

Well, it is not so week [sp.weak] if it is caused by spins. But spins themselves are relativistic and can be only understood properly from the Dirack [sp: Dirac] equation.

And yes, the energy is in the field. When a system of charged particles move, the energy of the particles + the field must be conserved.

Finally, we concur.

When you turn on a lignt bulb, where do you think those 100Watts go?

Let's presume that we're talking HID lighting, among the most efficient in current use.
E=I/R (Ohm's law) gets us on the right track. Most of the energy, alas, goes straight to ground. Only about 2.5% is emitted as heat, photons, and scalar field. Just because a light draws 100W, does not mean that you get 100W out. Also, observe the 4th root law for em radiation. Light decreases in intensity by the fourth root of its distance from the source.

Back to magnetic fields. Inductance laws still appply.

Same with magnetism.[/QUOTE]

 

[burashka]

When you turn on a lignt bulb, where do you think those 100Watts go?

Let's presume that we're talking HID lighting, among the most efficient in current use.
E=I/R (Ohm's law) gets us on the right track. Most of the energy, alas, goes straight to ground. Only about 2.5% is emitted as heat, photons, and scalar field. Just because a light draws 100W, does not mean that you get 100W out. Also, observe the 4th root law for em radiation. Light decreases in intensity by the fourth root of its distance from the source.

Actually, I was thinking of the most inefficient bulb you can imagine. 100Watts go all to radiation (thermal and otherwise) since there is no other significant cannel apart from some weak heat conductivity.

I don't understand what you mean by "go to the ground". The Joule's law applies to the filament and the energy is consumed from the power station by the filament. Then it heats up and starts to radiate.

 

[russ_watters]

When you turn on a lignt bulb, where do you think those 100Watts go?

Only about 2.5% is emitted as heat, photons, and scalar field. Just because a light draws 100W, does not mean that you get 100W out.

Only about 2.5% would go to light in an incandescent (without checking, that sounds about right), the rest does, in fact, go to heat. All 100 Watts is consumed and eventually it all ends up as heat (even the light, if your window shades are closed).

 

[burashka]

Only about 2.5% would go to light in an incandescent (without checking, that sounds about right), the rest does, in fact, go to heat. All 100 Watts is consumed and eventually it all ends up as heat (even the light, if your window shades are closed).

And where does the heat go, do you suppose?

 

[fedaykin]

"And where does the heat go, do you suppose?"

There are 3 main methods. Diffusion (spreading out via direct contact), convection (movement due to flow induced by density differential), and radiation (light).

The big problem with lightbulbs is that they emit much more infrared than visible light.

 

[burashka]

"And where does the heat go, do you suppose?"

There are 3 main methods. Diffusion (spreading out via direct contact), convection (movement due to flow induced by density differential), and radiation (light).

The big problem with lightbulbs is that they emit much more infrared than visible light.

Yes, exactly. In fact, most of the energy goes straight to radiation. I think I have said previously "visible and otherwise". Of course, we consider here the filament only. For the tiny wire that heats up inside the bulb, the mechanisms of heat transfer related to heat diffusion and convection (presumably, but the gases inside the bulb) are absolutely insignificant.

The point was that radiation must be included in the energy balance. Whenever electrodynamic interaction occurs and the EM energy of the initial and final states differ, you must take the radiation into account. Of course, this does not need to be visible radiation, or even infrared.

 

[fedaykin]

"Most of the energy, alas, goes straight to ground. Only about 2.5% is emitted as heat, photons, and scalar field. Just because a light draws 100W, does not mean that you get 100W out."

The lightbulb dissipates the power the flows across it. P=I^2*R
None of the power dissipated by the bulb goes to ground.

If a lightbulb draws 100W, and there is not reactive power (lightbulbs usually have very little), you will get 100W out. You might read up a bit on electric circuits. Most of the 100% (100W) is given out as heat, either through infrared or thermal conduction.