Magnetic force does not realize work

[intervoxel]

imagine a magnet on a table placed near a fixed solenoid. When the current in the solenoid is activated, the solenoid attracts the magnet performing work due to friction with the table.
how to admit in this case that the magnetic force didn't perform work since apparently there is a force times distance product?

 

[dgOnPhys]

No need to call in friction, when a magnetic dipole moves under the influence of a magnetic field, the magnetic field is performing work.

Remember in nature we have not only electric charges but also magnetic dipoles.

This (http://physicsinsights.org/force_on_dipole_1.html" ) might help

 

[Born2bwire]

The magnetic fields are incapable of doing work. However, due to the Lorentz transformation, a magnetic field in a lab frame may transform into both magnetic and electric fields in a moving frame. This electric field in the moving frame can do work via the Lorentz force. So while they do not directly do work, a moving charge or a time-varying magnetic field will give rise to additional electric fields that can do work. In the lab frame, where we only see magnetic fields, we will then observe energy to be extracted from the magnetic field.

 

[dgOnPhys]

I beg to differ: magnetic field performs work an magnetic dipoles. No need of calling in induction or relativity, it all happens within the realm of magnetostatics

 

[Born2bwire]

I beg to differ: magnetic field performs work an magnetic dipoles. No need of calling in induction or relativity, it all happens within the realm of magnetostatics

They don't, not directly. The only force equation we have is the Lorentz Force. A magnetic dipole is a loop current (the only sources in classical electrodynamics are charges and currents). With that in mind we once again find that the magnetic field does no work. But if we were to shift to a moving frame that becomes covariant with a moving charge in the dipole then we should find that the original magnetic field becomes transformed into both an electric and magnetic field. This electric field produces a Lorentz Force on the charge that allows for work to be done. In this manner we can extract energy from the magnetic field and transfer it to the dipole moment (and vice-versa) but this is implicitly done via an electric field at some point.

 

[sophiecentaur]

Isn't this just a matter of confusing force and work - along with the fact that there is energy involved in establishing a magnetic field? If you have an object, held stationary, as a magnetic field builds up, no work is done. Once you let the object go, if it moves then work is being done.
Am I being too simplistic here?

 

[Born2bwire]

Isn't this just a matter of confusing force and work - along with the fact that there is energy involved in establishing a magnetic field? If you have an object, held stationary, as a magnetic field builds up, no work is done. Once you let the object go, if it moves then work is being done.
Am I being too simplistic here?

But the equations governing the transfer of the energy state that the magnetic field cannot do any work. This comes up in lectures and Griffiths denotes explicitly in his textbook that the magnetic field cannot do work. This of course causes confusion because we know examples where we only have magnetic fields and work is done (ie: parallel current carrying wires). The solution lies in the field transformations that arise due to the changing of reference frames. In fact, this should be intuitively divined if you think about it. The Lorentz Force states that the electric fields give rise to a force on all charges but the magnetic field only creates a force on a moving charge. If we have a charge moving at a constant velocity through a magnetic field, then in the moving frame of the charge we suddenly have a charge at rest that must be experiencing a force. The conflict here is solved by finding that there is an electric field that is transformed from the original magnetic field in such a way that it acts on the stationary charge with the same force.

So the problem is intuitively we know that work must be done but we cannot see how this is done by the constituent equations of the theory. Only by understanding more about the relativistic properties and the physical behavior of the systems can we rectify this paradox.

People often use magnetic dipoles as a counter-example but this is flawed. First, magnetic dipoles are insufficient in rectifying situations where we have linearly moving charges (like in the parallel current carrying wires). Second, a magnetic dipole is not a primitive source in classical electrodynamics. Just like the electric dipole is actually two spatially separated opposite charges, a magnetic dipole is a loop current. These moments are nothing but far-field approximations of specific configurations of charges and moving charges. They are of course useful because many systems can be approximated as a configuration of moments and the electric dipole is the second lowest order electrical moment and the magnetic dipole moment is the lowest order magnetic moment. So if we take the magnetic dipole moment at it's face value of being a loop current, we are still left with the paradox that the Lorentz Force acting on this loop current does so in a manner such that the magnetic does not expend any work.

 

[cabraham]

They don't, not directly. The only force equation we have is the Lorentz Force. A magnetic dipole is a loop current (the only sources in classical electrodynamics are charges and currents). With that in mind we once again find that the magnetic field does no work. But if we were to shift to a moving frame that becomes covariant with a moving charge in the dipole then we should find that the original magnetic field becomes transformed into both an electric and magnetic field. This electric field produces a Lorentz Force on the charge that allows for work to be done. In this manner we can extract energy from the magnetic field and transfer it to the dipole moment (and vice-versa) but this is implicitly done via an electric field at some point.

Work is work. How can a mag field be doing work when viewed from one ref frame, but not from another? Also, the Lorentz force due to mag field is normal to the charge velocity. This results in zero work. But we are talking mag interaction between 2 dipoles.

When viewed mAcroscopically, the mag field certainly does work. But microscopically, it's more involved. The H field acts normal to the moving electrons in the wire. They are displaced. Then the E field between the electrons & lattice atomic nuclei results in a displacement due to electric force. The H field yanks on the electrons, then the lattice is tethered along due to E field force. The lattice neutrons are tethered along due to nuclear force, strong interaction.

So at the micro scale, it takes all 3 forces, H, E, & strong nuclear (SN), to displace wires. It's not just 1 or the other. The 3 work together in tandem. Just as H does no work on an electron, it is equally true that E does no work on a neutron. Since the entire wire, electrons, protons, & neutrons, gets displaced, no single force, E, H, or SN can account for this work.

Claude

 

[dgOnPhys]

...
People often use magnetic dipoles as a counter-example but this is flawed. First, magnetic dipoles are insufficient in rectifying situations where we have linearly moving charges (like in the parallel current carrying wires). Second, a magnetic dipole is not a primitive source in classical electrodynamics. ...

I guess that's one issue here: in my textbooks magnetic dipoles were primitive sources (as they are in nature).

Can we agree that once you have that then the magnetic fields can do work?

 

[Dickfore]

imagine a magnet on a table placed near a fixed solenoid. When the current in the solenoid is activated, the solenoid attracts the magnet performing work due to friction with the table.
how to admit in this case that the magnetic force didn't perform work since apparently there is a force times distance product?

The work was actually done by the source of emf which established the current in the solenoid.

 

[cabraham]

The work was actually done by the source of emf which established the current in the solenoid.

Of course. Even an E field cannot power a solenoid or motor. Whenever an E field does work on a charge, it loses some energy per conservation of energy law, CEL. The source providing power to the circuit is actually doing all the work. Fields are employed in order to focus & control the conversion of energy.

Claude

 

[Bob S]

The magnetic force due to static magnetic fields can be calculated by using the following formalism:

The total stored energy in a magnetic field is

W = ½∫B·H·dV = 1/(2μ₀)∫B²/μ·dV over all volume (and all magnetic materials with all permeabilities μ) containing magnetic field.

The force in direction x is

F_x = ∂W/∂x

The direction of the force is in a direction to increase W. Doing work F_xdx on a magnetic system decreases stored energy W. This opposite to mechanical systems like mgh.

When batteries and currents are involved, the batteries actually do the work.

Bob S