The Relationship between Magnets and Magnetic Forces

[Galois314]

I know that magnets produce magnetic fields (due to internal currents within the magnet). I also know that magnetic fields cannot do work on particles.

Given that, here is an apparent paradox I cannot fully understand: Consider a strong magnet and let us imagine bringing a small iron object next to the magnet. Then the magnet will exert a force that will attract the iron object towards it. This means the magnet is doing work on the iron object, which implies that this force astonishingly cannot be a magnetic force. But then, what is the nature of this force? It seems reasonable to expect this force to still be electromagnetic (even if it is not magnetic). Then, would this force be electric instead? If the force is electric, then it certainly cannot be electrostatic, which means that it has to be induced by a changing magnetic field (via Faraday's Law). If all of this is correct, then I am curious to how this changing magnetic field arises.

Thanks

 

[drvrm]

I also know that magnetic fields cannot do work on particles.

we find particles affected by magnetic fields in various experiments...how you know that ...?

 

[Dale]

I also know that magnetic fields cannot do work on particles.

This comes from Poynting’s theorem: $du/dt+\nabla\cdot S+J\cdot E=0$ where the last term is the work done on matter. Since it is $J\cdot E$ the B does not appear, so it is said that no work is done by the B field.

 

[PumpkinCougar95]

The magnetic Field does not do work on moving charges as the Magnetic Force is always Perpendicular to the Velocity and hence Power is Zero (P = F.v)

According to me the No uniform magnetic field magnetises the iron nail and induces a Dipole in it. Since the field is non-uniform there is a force along with a torque on that dipole.

Edit: Here the induced north and south poles are far apart that is why there is a force.(You can calculate the force by assuming magnetic charges which don't really exist)

 

[Jano L.]

I know that magnets produce magnetic fields (due to internal currents within the magnet). I also know that magnetic fields cannot do work on particles.Given that, here is an apparent paradox I cannot fully understand: Consider a strong magnet and let us imagine bringing a small iron object next to the magnet. Then the magnet will exert a force that will attract the iron object towards it. This means the magnet is doing work on the iron object, which implies that this force astonishingly cannot be a magnetic force. But then, what is the nature of this force? It seems reasonable to expect this force to still be electromagnetic (even if it is not magnetic). Then, would this force be electric instead?

There are two ways to understand the magnetic attraction and resolving the 'magnetic force does no work' problem.

The first one is to use the magnetic pole description of matter, where magnets are modeled as collection of equal number of positive and negative magnetic pole that interact via Coulomb forces. This is a very common and useful approach to understand material magnetism. The 'no work theorem' holds only for Lorentz force acting on a charged particle, it does not hold for magnetic force acting on magnetic monopole or magnetic dipole.

The other one is to say there are no magnetic poles, only electric ones and magnetic effects of magnets are due to microscopic electric currents inside them. Then the problem with 'no work theorem' is a real one and needs addressing.
You are right that if it isn't magnetic forces which do work, then it has to be electrical forces. But if it was the "induced" electric forces, their magnitude and so the magnitude of work done would depend on the speed with which the iron object is approaching the magnet. But from experience we know that is not so -- the work per displacement is, to a first approximation, independent of how fast the iron object is allowed to move (this is true only for small velocities but it is the common situation).

The electric forces involved in doing the work have the character of conservative forces that depend on the position of the iron object with respect to the magnet, i.e. forces of electrostatic field.

However, it cannot be the electrostatic field of the magnet, since we know there is no noticeable field between the magnet and the iron object; there is no way magnet can create electrostatic field only in the limited region of space where the attracted object is, without leaking it also into the interspace.

So, what other electric forces can there be that could be localized in the iron body but without any field being between the magnet and the body?

They are the internal electric forces, acting due to one particle of iron body on another. These internal forces do work on the iron body and impart it either kinetic energy or (if we do not let that happen) do work on whatever is holding the iron back.

I can see this may sound ridiculous -- how can internal forces move the body? What about conservation of momentum?

But it is fine. The momentum is not conserved here, because of the external magnetic forces due to the magnet. The kinetic energy though, is not conserved because internal electric forces can do net work on the body - they change EM field energy into kinetic energy of the iron object.

It is like when you jump off the ground - all the work that is done is due to internal forces between your muscles and bones and the rest of the body (the analogue of charged particles of the iron). The ground (the analogue of the magnet) does no work at all, because the thing it acts on - the feet - have zero velocity (the magnetic force is perpendicular to velocity). But the ground (magnet) is necessary to get the human body (iron body) move as a whole (to act with external force to change the momentum).

In short, internal electrostatic forces cannot change momentum of the body (they cancel by pairs their impulse effects), but they can change total kinetic energy (the works done by the forces in the pair do not cancel). Formally,

$\mathbf F_{i}(\mathbf r_j) = - \mathbf F_{j}(\mathbf r_i),$

but
$\mathbf F_{i}(\mathbf r_j) \cdot \mathbf v_j \neq - \mathbf F_{j}(\mathbf r_i)\cdot\mathbf v_i.$

 

[Dale]

The 'no work theorem' holds only for Lorentz force acting on a charged particle,

Poynting’s theorem (as I wrote it above) can be derived from Maxwell’s equations. So it holds any time they hold.

These internal forces do work on the iron body

Internal forces cannot do work on a system. Work is a transfer of energy, so internal forces can only move energy around within a system. For example, changing chemical to kinetic energy in a rocket.

In the case of the magnetic field there is a decrease in the energy of the B field, and no decrease of the internal energy. So the internal force approach doesn’t match.

Here is a different approach that I have looked into personally:
https://www.physicsforums.com/threads/work-term-in-poyntings-theorem.826177/#post-5188464

I think it is correct, but I haven’t seen it derived elsewhere so I cannot assert its validity.

 

[Jano L.]

Poynting’s theorem (as I wrote it above) can be derived from Maxwell’s equations. So it holds any time they hold.

Sure, but the Poynting theorem on its own implies nothing about what the expression for EM force acting on a particle is, or what the expression for work of that force is. The former depends on the model of forces - in the Ampere tradition, the magnetic force is always perpendicular to velocity, in the Coulomb model of magnetism, there is no such condition.

Internal forces cannot do work on a system. Work is a transfer of energy, so internal forces can only move energy around within a system. For example, changing chemical to kinetic energy in a rocket.

In the case of the magnetic field there is a decrease in the energy of the B field, and no decrease of the internal energy. So the internal force approach doesn’t match.

Internal force due to particle 1 on particle 2 does work on the particle 2 when that force has component along particle 2 velocity. Sum of these works manifests as increase in total kinetic energy of the system of particles and can be called work of internal forces. This energy decreases EM energy in the region containing both magnet and the iron object. It does not decrease the internal potential energy of the particles of the iron body, only the interaction energy between the magnet and the iron.

Here is a different approach that I have looked into personally:
https://www.physicsforums.com/threads/work-term-in-poyntings-theorem.826177/#post-5188464

I think it is correct, but I haven’t seen it derived elsewhere so I cannot assert its validity.

I'll have a look later this day.

 

[Dale]

Internal force due to particle 1 on particle 2 does work on the particle 2 when that force has component along particle 2 velocity. Sum of these works manifests as increase in total kinetic energy

It must be associated with a decrease in some other form of internal energy. This is not the case here.

It does not decrease the internal potential energy of the particles of the iron body, only the interaction energy between the magnet and the iron

Then it cannot be due to internal forces. The work must be due to the interaction between the magnet and the iron.

If you wish to continue pushing this viewpoint, please provide a professional scientific reference corroborating the approach

 

[Jano L.]

It must be associated with a decrease in some other form of internal energy.

If the work is done too quickly, yes. But if it is done in a quasi-static manner, the decrease of internal energy can be made arbitrarily small, far less than the work done, because the system(iron body) is not isolated.

In general, macroscopic systems in interaction with other systems can do work without any change in their internal energy. Consider a more familiar example: isothermal expansion of ideal gas in a cylinder with piston. The gas does net work on its outside but its internal energy does not change. That is possible because while energy is coming out through the piston, it is also coming in through the diathermal walls as heat. The energy to do the work comes from the outside.

Similar thing may be happening in the magnet and iron body situation (although there are some important differences): while the iron body very slowly moves towards the magnet and does work on the body that is holding it back, any energy expended on that does not seem to manifest in any decrease of internal energy of the iron body or the magnet. If some internal energy is temporarily used for that, it has to be quickly resupplied so we do not observer any noticeable decrease. The obvious source is the EM energy from outside the iron body (actually, probably the energy is oversupplied since the macroscopic field inside the iron body increases).

So to summarize, body 1 can do work without other body 2 doing work on the body 1, without change in internal energy of either of them, provided there is another supply of energy. In our case, the source of energy is EM energy in the space around the bodies.

The work must be due to the interaction between the magnet and the iron.

Indeed, it is "due to interaction", because without the magnet, the iron body does not move.

But the work can't be "equal to work of forces of the magnet acting on the iron body", because those do no work.

Just as in the gas example, the work is due to interaction of the gas walls with the heat reservoir, but it is not equal to work of the forces of pressure of the reservoir on the walls, because those do no work.

Back in the magnet and iron case, the work is due to forces of the iron body, the necessary energy comes from the EM energy outside of the body.

If you wish to continue pushing this viewpoint

Not at all, I don't mean to be pushy. Just trying to discuss it with people who like to do the same.

 

[Dale]

Not at all, I don't mean to be pushy. Just trying to discuss it with people who like to do the same.

I don’t think these vague hand waving speculations are appropriate here, and I am very skeptical of their validity, and so far you have provided no reference nor math to support the claim.

 

[Tom.G]

@Jano L. Following you line of reasoning, couldn't your arguments equally apply to two identically charged particles being accelerated away from each other due to mutual repulsion?
How about two oppositely charged particles being accelerated toward each other due to mutual attraction?

 

[drvrm]

I don’t think these vague hand waving speculations are appropriate here, and I am very skeptical of their validity, and so far you have provided no reference nor math to support the claim.

i saw a paper and just thought it may help the discussion...

Magnetic Forces Can Do Work Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (April 10, 2011; updated Dec. 11, 2015)

ref. http://www.hep.princeton.edu/~mcdonald/examples/disk.pdf

 

[Jano L.]

@Jano L. Following you line of reasoning, couldn't your arguments equally apply to two identically charged particles being accelerated away from each other due to mutual repulsion?
How about two oppositely charged particles being accelerated toward each other due to mutual attraction?

I am not sure what you mean. My reasoning attempts to answer the question : which forces do the work on the iron body when it is attracted to the magnet.

If we have just two charged particles and no magnet, then the original question does not arise.

If you are wondering where the increase of kinetic energy of particles comes from, it comes from the EM interaction energy of the particles. The work is done, again, by the mutual electric forces between the particles.