Magnetic fields do no work? How come

[elliotr]

According to every textbook I know of, magnetic forces do no work (e.g. David Griffiths Pg. 207). Yet this problem causes this to be hard to believe:

If I take two magnets, I can set them down on a table (with a little friction). I then slowly push them toward each other, then at some point, the two magnets attract and move toward each other. That is, two magnets appear to exert a force on each other, and this force is exerted over the distance it takes to make contact (even with a little friction). Surly something is doing work to at least counteract the friction, if not cause non-zero mass magnets to accelerate.

How can you tell me that magnetic forces do no work? These two magnets appear to do work, as far as I can tell.

This problem has bothered me for a long time. Please explain!

Thanks.

 

[Nabeshin]

Haven't read Griffiths at all so I'm not sure exactly what he's talking about, but this statement is usually made with regards to the magnetic force on a charged particle. In this case, it's pretty trivial to show since velocity and force are perpendicular.

 

[elliotr]

Quote: "Magnetic Forces do no work" in bold, in a box, in the middle of the page.

But between two magnets, what forces other than magnetic forces exist? What force causes them to move together?

Thanks

 

[Pengwuino]

I believe I remember what Griffiths was talking about. I think he was talking about how an electron or current would gain energy but from where? He should have specifically stated that the energy comes from whatever is maintaining that magnetic field. I know he explained it... wonder where my copy is and if it still hasn't fallen apart.

 

[elliotr]

A better question: "Can a magnet (e.g. a permanent magnet) do work?"

If no: how do magnets move together appearing to do work? What's actually doing the work (see first question).

If yes: how is this possible when "magnetic forces do no work"?

 

[Phrak]

While you have two stationary magnets, obviously no work is done, one on the other.

A magnet, in moving, posesses an electric field.

 

[elliotr]

That's a very good point. But let's say that I bring the magnets to a halt after I feel the force of magnets wanting to move toward each other. At this point, the magnets are not moving, so no electric field exists. Yet when I let go, they will still move toward each other.

 

[Phrak]

That's a very good point. But let's say that I bring the magnets to a halt after I feel the force of magnets wanting to move toward each other. At this point, the magnets are not moving, so no electric field exists. Yet when I let go, they will still move toward each other.

It is late for me, and this is my last post. I think you are questioning the disparity--work is done by the electric fields. But the force developed, when the magnets are stationary, is magnetic. So how is this resolved?

Wonderful question!

I'm sorry not to answer at this time.

 

[kmarinas86]

According to every textbook I know of, magnetic forces do no work (e.g. David Griffiths Pg. 207). Yet this problem causes this to be hard to believe:

If I take two magnets, I can set them down on a table (with a little friction). I then slowly push them toward each other, then at some point, the two magnets attract and move toward each other. That is, two magnets appear to exert a force on each other, and this force is exerted over the distance it takes to make contact (even with a little friction). Surly something is doing work to at least counteract the friction, if not cause non-zero mass magnets to accelerate.

How can you tell me that magnetic forces do no work? These two magnets appear to do work, as far as I can tell.

This problem has bothered me for a long time. Please explain!

Thanks.

Virtually anything capable of doing work involves a carrier of energy. Mostly this involves the electrostatic repulsion between particles (e.g. rocket vs. exhaust, tires vs. road, feet vs. floor, etc.). In other cases you have magnetic fields such as can be found in magnetic levitation trains and linear induction motors in modern roller coaster rides. Carriers of energy do not do the work, they simply deliver the energy.

Energy ultimately comes from utilizing charge potential, be it nuclear or chemical. Even solar energy is derived this way. There is no other way of adding energy into a system, period. Everything else is simply the hot potato-ing of this energy.

 

[Dadface]

An energy transfer is needed to change the separation of two magnets or a magnet and an unmagnetised magnetic material.When attracting magnets are pulled further apart or when repelling magnets are pushed closer together an energy input is needed and there is a change of magnetic field with a resulting increase of potential energy.The stored energy can then do work to push/pull the magnets back in the opposite direction.Like others I think the book was referring to the magnetic force on moving charged particles, in which case the field does no work.

 

[kmarinas86]

An energy transfer is needed to change the separation of two magnets or a magnet and an unmagnetised magnetic material.When attracting magnets are pulled further apart or when repelling magnets are pushed closer together an energy input is needed and there is a change of magnetic field with a resulting increase of potential energy.The stored energy can then do work to push/pull the magnets back in the opposite direction.Like others I think the book was referring to the magnetic force on moving charged particles, in which case the field does no work.

So is it true that no work is being done on charged particles in the sun's corona? They are not gaining kinetic energy?

Obviously it can't be the magnetic field. It must be some other force.

So their trajectory is determined by nuclear fusion?

I don't think so...

Sunspots are not produced by magnetism? Obviously no work was done by the Lorentz force to produce those. They're really a byproduct of a combination of fusion and gravity.... ?

GIVE ME A BREAK!

 

[Bob S]

Here is an interesting experiment. Use a permanent magnet (PM) and build a solenoid magnet about the same size. Use low resistance wire. Power the solenoid with a constant-current source (you can use two npn transistors and a resistor). Put a voltmeter across the solenoid. Move the PM quickly up to, or away from the solenoid. Do you see a voltage pulse on the voltmeter? Why? What is the approximate volt-seconds? The energy (joules) is the volt-sec times the solenoid current. Where is this energy coming from, or going to? (If the voltage pulse is the same sign as the current, the current regulator is doing work. If the sign is opposite, the current regulator is absorbing energy.)
Bob S

 

[Vanadium 50]

I don't like teaching the meme "magnetic fields do no work." It is true, but it is not useful.

It's clearly true for a single charged particle: the Lorentz force law has the magnetic force perpendicular to the direction of motion, so the dot product of force and displacement is always zero. It's also clearly true that magnets can do work on each other.

The solution to this apparent contradiction is that complex objects like magnets are made up of many charges, and these charges exhibit both electric and magnetic forces on each other, and if one does the calculation carefully enough, it can be shown that the work actually comes from these (usually internal) electric forces.

So what do you gain by thinking about things this way? To my mind, very little: you're trading a relatively simple calculation - say the torque on a magnetic dipole in a magnetic field - for a very complicated one involving internal electric forces. This seems like a poor trade. Note that I am not arguing that "magnetic fields do no work" is not true. I am arguing that it is not useful. It's (relatively recent) overemphasis is not, in my mind, a good thing.

As far as the solar corona, I am not a solar physicist, but I do want to point out that the sun's magnetic field is far from static, and a changing magnetic field produces an electric field, and electric fields can do work.

 

[Dadface]

I hope I am summarising the majority of different responses here correctly.
1.Work can be done on or by magnetic fields.
2.Work can be done on or by electric fields.
3.There is no work done by the Lorentz force on charged particles.

I think that it's point 3. that the textbooks elliotr is using referred to and it would be instructive to see a relevant quote from the book so that the question can be answered in context.

kmarinas 86 will you please clarify your post(11) where you seem to imply that as far as stellar events are concerned work is,in fact, done by the Lorentz force.This force is highly instrumental in determining the paths of the particles,it can accelerate the particles by changing their directions but how,for example,can this force,on its own, change their kinetic energies?

 

[lugita15]

I think the core problem at issue can be illustrated with a superficially different example. Consider two parallel current carrying wires. Each will have an attractive magnetic force on the other, and so the two wires will come closer together. Since the magnetic force is in the same direction as the direction of motion, work is being done by the magnetic force.

So how is this possible?

 

[diazona]

The magnetic force in that case just acts on the electrons that are moving through each wire. It tries to bend the trajectories of the electrons in one wire toward the other wire, and vice versa. No work is involved in that part. But the electrons attract the positively charged atomic nuclei in the wire by the electric force, and that force does the work of moving the wire.

Whenever it looks like magnetic forces are doing work, if you think about it closely enough it actually turns out to be the electric force.

 

[kmarinas86]

The magnetic force in that case just acts on the electrons that are moving through each wire. It tries to bend the trajectories of the electrons in one wire toward the other wire, and vice versa. No work is involved in that part. But the electrons attract the positively charged atomic nuclei in the wire by the electric force, and that force does the work of moving the wire.

Whenever it looks like magnetic forces are doing work, if you think about it closely enough it actually turns out to be the electric force.

If that is true, then the forces in question should not behave differently in relativistic scenarios. But if they do, we should called it the electromagnetic force instead.

 

[cabraham]

The magnetic force in that case just acts on the electrons that are moving through each wire. It tries to bend the trajectories of the electrons in one wire toward the other wire, and vice versa. No work is involved in that part. But the electrons attract the positively charged atomic nuclei in the wire by the electric force, and that force does the work of moving the wire.

Whenever it looks like magnetic forces are doing work, if you think about it closely enough it actually turns out to be the electric force.

Not! A magnet held over a paper clip lifts said clip by magnetic force, NOT electric force. The clip is increased in potential energy. The magnetic force did the work, not the electric.

With 2 wires carrying current, the mag force is responsible for the interacting force between the wires, NOT electric.

Any peer-reviewed text will elaborate.

Claude

 

[Phrak]

Not! A magnet held over a paper clip lifts said clip by magnetic force, NOT electric force. The clip is increased in potential energy. The magnetic force did the work, not the electric.

With 2 wires carrying current, the mag force is responsible for the interacting force between the wires, NOT electric.

Any peer-reviewed text will elaborate.

Claude

I don't know what stimulated this excited response, but it wasn't through careful analysis.

This problem is better analysed by a replacement analogy where we can deal with things we can better understand. Replaced the permanent magnet with a solenoid and the paper clip with an array of wire loops.

The electric field, not the magnetic field is responsible for the work done.

Can you see that the electric field of the permanent magnet is responsible for the work done on the paper clip in the inertial frame of the paper clip? A changing magnetic field produces an electric field. This should be quantified in any text that covers dynamic electromagnetism.

 

[Phrak]

I hope I am summarising the majority of different responses here correctly.
1.Work can be done on or by magnetic fields.
2.Work can be done on or by electric fields.
3.There is no work done by the Lorentz force on charged particles.

Where are the mentors?

1. 1. is wrong.

3. 3. is wrong. You need to look up the Lorentz force

 

[kanato]

Playing devil's advocate here, there are a couple of obvious objections I see to that analysis:

In the laboratory reference frame, it seems pretty clear that the magnetic field from the solenoid is constant, so there is no electric field, and the work done on the paper clip is caused by the magnetic field in that frame. Since analysis in any reference frame is equivalent to any other reference frame, I don't see why it is invalid to say magnetic fields do work.

The rest frame of the paper clip is non-inertial, so that complicates the analysis. Also, there is both a magnetic and electric field in that frame, so it's not clear that the electric field is responsible for the force. Especially since there will be an induced current in the paper clip, which will experience a force from the magnetic field.

 

[kanato]

I'm reminded of another objection:

Usually the argument that the magnetic field does no work is made by boosting to a frame where the current is zero, so the only force can come from the electric field. But consider an electron in a static magnetic field with a gradient. The electron has a permanent magnetic dipole moment, so it will feel a force from the magnetic field. There is no reference frame you can boost to where either the magnetic field disappears, or the magnetic dipole of the electron disappears (I think). So in every possible inertial frame, there is a contribution to the force that comes purely from the magnetic field.

 

[diazona]

Playing devil's advocate here, there are a couple of obvious objections I see to that analysis:

In the laboratory reference frame, it seems pretty clear that the magnetic field from the solenoid is constant, so there is no electric field, and the work done on the paper clip is caused by the magnetic field in that frame. Since analysis in any reference frame is equivalent to any other reference frame, I don't see why it is invalid to say magnetic fields do work.

Actually there is an electric field produced by the charged particles that make up the paper clip. That's the field that directly does the work. Roughly speaking, the magnetic field only alters the motion of electrons so that they are in a position to do work.

I'm reminded of another objection:

Usually the argument that the magnetic field does no work is made by boosting to a frame where the current is zero, so the only force can come from the electric field. But consider an electron in a static magnetic field with a gradient. The electron has a permanent magnetic dipole moment, so it will feel a force from the magnetic field. There is no reference frame you can boost to where either the magnetic field disappears, or the magnetic dipole of the electron disappears (I think). So in every possible inertial frame, there is a contribution to the force that comes purely from the magnetic field.

The electron in that case would feel a torque, not a force, from the interaction of its magnetic dipole moment with the magnetic field.

 

[Dadface]

I hope I am summarising the majority of different responses here correctly.
1.Work can be done on or by magnetic fields.
2.Work can be done on or by electric fields.
3.There is no work done by the Lorentz force on charged particles.

I think that it's point 3. that the textbooks elliotr is using referred to and it would be instructive to see a relevant quote from the book so that the question can be answered in context.

kmarinas 86 will you please clarify your post(11) where you seem to imply that as far as stellar events are concerned work is,in fact, done by the Lorentz force.This force is highly instrumental in determining the paths of the particles,it can accelerate the particles by changing their directions but how,for example,can this force,on its own, change their kinetic energies?

Where are the mentors?

1. 1. is wrong.

3. 3. is wrong. You need to look up the Lorentz force

I suppose one out of three is better than nothing.You have me particularly confused with your answer to point number three.I took your advice and I looked up the Lorentz force and everything I have read so far, but this is only via google and not peer reviewed publications, seems to confirm what I thought I already knew and understood...because there is a zero component of motion in the direction of the force then by definition the work done is zero.If this is wrong then I would appreciate it if you could provide me with a suitable reference that I could look up.
I also take some issue with your answer to point number one,and as I see it so far(but I am still thinking about this) work can be done by say two permanent magnets or a permanent magnet and a ferromagnet.I think some good examples of this have been given in this thread.Is it a valid exercise to consider an electromagnet as being equivelent to a permanent magnet?At the moment I have very strong reservations about this not the least reason being that the internal mechanisms responsible for creating the fields are different this,possibly,resulting in differences in the fields themselves.

 

[cabraham]

I don't know what stimulated this excited response, but it wasn't through careful analysis.

This problem is better analysed by a replacement analogy where we can deal with things we can better understand. Replaced the permanent magnet with a solenoid and the paper clip with an array of wire loops.

The electric field, not the magnetic field is responsible for the work done.

Can you see that the electric field of the permanent magnet is responsible for the work done on the paper clip in the inertial frame of the paper clip? A changing magnetic field produces an electric field. This should be quantified in any text that covers dynamic electromagnetism.

The permanent magnet field is static, not changing. The instant the paper clip is attracted and begins moving towards the magnet it is feeling magnetic, not electric force. This is a static condition, not time vasrying.

Motors have electric fields as well as magnetic. But the E forces are much too weak to produce the motor action. The H forces are way stronger. Of course a time changing H will always be accompanied by an E field as well, since they are inclusive (time changing conditions).

The force betwen 2 wires is magnetic. The notion that H fields do no work is only under specific conditions. A charged particle, an electron, will move in the same direction as E, but normal to H. Thus E can do work on the e-, whereas H does not. H only changes the e- direction.

But 2 wires can be attracted/repulsed due to H. The mag force is published in every reference. The definition of the ampere unit is based on 2 wires and the force incurred when carrying current. The fact that 2 wires carrying currents in opposite directions incur a repulsive force cannot be explained with E fields, but is perfectly consistent with H fields.

Just use the right hand rule and see what I mean. Every text cannot be wrong. If what you say is true, why doesn't every university teach it? These questions have been under scrutiny since the 19th century. It's a bit presumptuous to think that all the physics & EE curriculums have had it wrong for 2 centuries, and that you have the right answer.

As far as reference frames & relativity goes, we don't need to go there. This can be explained with classic e/m fields.

Claude

 

[kanato]

Actually there is an electric field produced by the charged particles that make up the paper clip. That's the field that directly does the work. Roughly speaking, the magnetic field only alters the motion of electrons so that they are in a position to do work.

In the reference frame of the paper clip, there is a current from the charged particles moving, so there is a magnetic force which does work. There may also be an electric field, but there is still a magnetic force.

The electron in that case would feel a torque, not a force, from the interaction of its magnetic dipole moment with the magnetic field.

Two comments: 1) the torque of a magnetic field $$\vec{\tau} = \vec{\mu} \times \vec{B}$$ does work; any elementary text should write down the potential energy $$U = -\vec{\mu} \cdot \vec{B}$$ (indicating a conservative force and therefore it can do work), and 2) I specifically mentioned that the B field has a gradient, and in a non-uniform field a magnetic dipole will experience a force as well as a torque. This is why magnets are attracted to each other in a laboratory reference frame.

 

[Bill Foster]

$$\textbf{F}=q\left(\textbf{E}+\textbf{v}\times\textbf{B}\right)$$
$$\int{\textbf{F}\cdot d\textbf{l}}=q\left(\int{\textbf{E}\cdot d\textbf{l}}+\int{\textbf{v}\times\textbf{B}\cdot d\textbf{l}}\right)$$
$$W=q\int{\textbf{E}\cdot d\textbf{l}}$$
$$\frac{W}{q}=\int{\textbf{E}\cdot d\textbf{l}}$$
$$V=\int{\textbf{E}\cdot d\textbf{l}}$$

 

[cabraham]

$$\textbf{F}=q\left(\textbf{E}+\textbf{v}\times\textbf{B}\right)$$
$$\int{\textbf{F}\cdot d\textbf{l}}=q\left(\int{\textbf{E}\cdot d\textbf{l}}+\int{\textbf{v}\times\textbf{B}\cdot d\textbf{l}}\right)$$
$$W=q\int{\textbf{E}\cdot d\textbf{l}}$$
$$\frac{W}{q}=\int{\textbf{E}\cdot d\textbf{l}}$$
$$V=\int{\textbf{E}\cdot d\textbf{l}}$$

I already stated that this is for a single particle. A current in a wire has an H field in addition to an E field. I'm at work and can't elaborate, but the math for the magnetic force between 2 wires with current is needed.

The H field does no work on an electron. The Lorentz force law is universally known. Some are trying to generalize by saying that the force between 2 wires w/ current is not magnetic, but electric. Impossible.

The right hand rule comes to mind. Also, how can one explain using E only and not H, the following. When the 2 currents in the wires are in the same direction, the wires attract. In opposite directions, the wires repel. You cannot explain that with E fields, but with H fields and the right hand rule it's all too easy.

Please start 'splaining.

Claude

 

[Phrak]

You have me particularly confused with your answer to point number three. I took your advice and I looked up the Lorentz force and everything I have read so far, but this is only via google and not peer reviewed publications, seems to confirm what I thought I already knew and understood...because there is a zero component of motion in the direction of the force then by definition the work done is zero.If this is wrong then I would appreciate it if you could provide me with a suitable reference that I could look up.

Sorry. I was getting a little punchy--and inacurate.

Try googling force on magnetic dipole.

 

[kmarinas86]

Actually there is an electric field produced by the charged particles that make up the paper clip. That's the field that directly does the work. Roughly speaking, the magnetic field only alters the motion of electrons so that they are in a position to do work.


The electron in that case would feel a torque, not a force, from the interaction of its magnetic dipole moment with the magnetic field.

Torque is the vector cross product of force and turning radius. That is absolute and final.

Signed,

Kmarinas86

 

[kmarinas86]

The right hand rule comes to mind. Also, how can one explain using E only and not H, the following. When the 2 currents in the wires are in the same direction, the wires attract. In opposite directions, the wires repel. You cannot explain that with E fields, but with H fields and the right hand rule it's all too easy.

Please start 'splaining.

Claude

None of these people want to do that.

Sad...

 

[Doc Al]

The right hand rule comes to mind. Also, how can one explain using E only and not H, the following. When the 2 currents in the wires are in the same direction, the wires attract. In opposite directions, the wires repel. You cannot explain that with E fields, but with H fields and the right hand rule it's all too easy.

Please start 'splaining.

That's an easy one. The magnetic field from one wire deflects the charge carriers (the electrons) in the other wire to one side, creating a static electric field which exerts a force on the positive lattice of the wire. That force pulls the wires together.

None of these people want to do that.

Sad...

I guess you don't understand it either. How sad!

 

[cabraham]

That's an easy one. The magnetic field from one wire deflects the charge carriers (the electrons) in the other wire to one side, creating a static electric field which exerts a force on the positive lattice of the wire. That force pulls the wires together.


I guess you don't understand it either. How sad!

Would you please elaborate on the direction of the said field and lattice polarization? Let's use cylindrical coordinates. Current in both wires is in the +z direction in case 1. In case 2, currents are in the +z & -z directions.

Case 1) I did a scratch diagram on a post it note. I'll sketch a nice diagram at home tonight and post it. In my quick off the cuff analysis, for 2 currents in the +z direction, the electrons shift towards the exterior of the wire pair per the Lorentz force law relation. This would result in a repulsive force considering only the E field. But we know that like currents attract, not repel. I don't think the E field contribution to the force is nearly as much as the H field.

Both are present and exert influence, but H is clearly the stronger of the two. Again, I'm at work, so I won't make an absolute pronouncement till I get home tonight. You could be right, but it looks like you're not.

Case 2) The same as case 1) with polarites reversed. Again, it appears that the force is opposite to what you describe. The electrons are shifted to the interior of the wire pair, again resulting in a repulsive force. Of course, the wires do repulse, but the E fields seem to produce repusion regardless of the polarity of the currents. The H fields using the right hand rule are consistent with observation.

Is there something I've overlooked? It appears that the repulsive/attractive forces due to currents in the 2 wires is strongly determined by H, and only weakly a function of E. If I've erred, please let me know.

Claude

 

[Doc Al]

Case 1) I did a scratch diagram on a post it note. I'll sketch a nice diagram at home tonight and post it. In my quick off the cuff analysis, for 2 currents in the +z direction, the electrons shift towards the exterior of the wire pair per the Lorentz force law relation.

They shift towards the interior. (They move opposite to the conventional current.)

 

[cabraham]

They shift towards the interior. (They move opposite to the conventional current.)

Sure. But does that change anything? With 2 currents in the same direction, the electrons shift inward creating a repulsive force between the 2 wires. But we observe that the force is attractive. How?

Answer - there are both electric and magnetic components of force. The mag is much stronger. In machines class this was repeated often. What you're saying is not what is being disputed. What lies at the heart of this is that the H field attraction exists in addition to the E field attraction. Both are present, but the force due to H is stronger than that due to E.

It's quite obvious that one cannot equate this 2 wire system attractive force with that of electron-positive-ion electric field interaction. It's basically magnetic in nature. Later tonight, I'll post a detailed diagram. BR.

Claude