# I know magnetic forces do no work, but

1. May 24, 2006

### ptabor

if I set a bar magnet down next to a small metallic object, the object is displaced. Clearly, through this displacement energy is being expended (to overcome the kinetic friction to keep it moving for some distance).

So what is doing the work here?

Is it whatever mechanism gave rise to the magnetic field of the bar magnet in the first place?

2. May 24, 2006

### ptabor

or wait...
as I use my hand to bring the magnet closer to the object, this creates a changing magnetic flux which induces an electric field.
So then it would be the induced electric field that exerts the force on the object.

So I guess that means that I'M doing the work?

3. May 24, 2006

### Quaoar

Bingo. :shy:

4. May 24, 2006

### jasc15

5. May 24, 2006

### LeonhardEuler

You are not doing the work on the object since you are not touching it. Another way to think about this is with two metal wires with no current initially flowing through them. Then a switch is flipped and current flows causing magnetic fields that attract the wires to one another. In this case it is clear that there is no one around to be doing the work. I've thought about this very question myself and here is the idea I have come up with to explain it. I'm not sure its right but it makes sense to me:

The magnetic field causes the electrons travelling in the wire to change direction. No work is done because the electrons change direction only and not speed. This forces the electrons to the edge of the wire. Most of the electrons can not leave the wire because that would leave a positive charge behind and attract them back. The attraction of the slightly positively charged wire to the electrons causes the entire wire to be attracted to the other wire, increasing the wire's speed. Thus it is actually the electric force which does the work on the wire.

This is the explaination makes sense to me. What do people think?

6. May 24, 2006

### ptabor

"In this case it is clear that there is no one around to be doing the work."

In this case it is easy, though. The work is being provided by the battery, or the generator that supplies the current.

You are correct, however, it is the electric field which is exerting the force, over some distance parallel to the displacement.

I think your reasoning for the electrons being confined to the wire is incorrect. The electrons can't leave the wire because the potential barrier is practically infinite. The potential barrier is provided by an insulating material, which does not allow the conduction of electrons.

In addition, you do not have to touch an object to do work on it. Work is clearly being done on an object in freefall, however there is no contact. In this case, the gravitational field of the earth is exerting a force and doing the work. This is your classic action at a distance notion, that is typical of the newtonian view.

7. May 24, 2006

### LeonhardEuler

Right, the gravitational field is doing the work. But if you want to do work with a normal force you must be in contact with the object. (Or practically in contact with the object, since it is actually the result of electrostatic interactions at a very small distance). As far as the "insulating material", the wires could be bare and in a vacuum and there would be no insulating material, and the same effect would still be observed.

When you say that the battery does the work, that is correct in some sense but I think we are arguing over semantics. The battery drives the current through the circuits, which then generates the magnetic fields, which then has an electric effect. So it is only indirectly that the battery does the work of attracting the wires.

8. May 24, 2006

### fargoth

its pretty easy to see if the battery does the work:
get two wires, connect them to batteries and check whether the current changes when the wires are closer...

uhm, and what did you mean when you said magnetic forces do not work?
force is a gradiant of potential energy, and ofcourse two magnetic dipoles have a potential energy slope between them - hence force...
when a rock and the earth falls into each-other, who did the work? if gravitation is your answer, then when two magnetic dipoles fall into each-other the magnetic field did the work...

Last edited: May 24, 2006
9. May 24, 2006

### LeonhardEuler

His point is that the magnetic force is $\vec{F}=q\vec{v}\times\vec{B}$ which is always directed perpendicular to the velocity, therefore the magnetic force can do no work.

Also, everyone agrees the battery does work, just not that the EMF of the battery is the actual force that directly attracts the wires.

10. May 24, 2006

### fargoth

oh, he was talking about the Lorentz force... but thats not what attracts metal to a magnet bar... atleast not the way you pictured it with electrons which start to move around because of induced current and attract the metalic body to the magnet bar...

it is the force that attracts the two wires though...

the explanation lies in quantum mechanics, i tried to explain it here, but re-read my explanation and found it hard to understand... so i suggest you read a little about paramagnetism and ferromagnetism...

in general, the force that the metal feels is, like i said earlier, is the gradiant of the energy (with an opposed sign).
the dipoles in the metal and magnet aren't caused by electrons moving in there in the classical sense... so Lorentz force isn't the appropriate way to look at it...
to calculate the force between two dipoles just find the potential energy of two magnetic dipoles on each other: $$U=-mB=\frac{m^2\sqrt{1+3sin^2(\Theta)}}{r^3}$$
now just derive the force from here... this force is in the direction of movement and it does the work...

Last edited: May 24, 2006
11. May 24, 2006

### fargoth

i could have sworn i saw a post after my first one explaining what the OP meant... maybe im starting to see things

12. May 24, 2006

### Integral

Staff Emeritus
You are not. The missing posts are being reviewed by the mentors.

13. May 24, 2006

### Staff: Mentor

I "undeleted" LeonhardEuler's posts. He's correct about what he was explaining--that a magnetic field does not directly do work on a moving charge (like a current carrying wire): the work is actually being done by an induced electric field.

Of course, as fargoth correctly explains, that's not what's going on when a magnet attracts a piece of metal. In that case, it's not a matter of a magnetic field acting on a moving charge, but a magnetic field acting on the intrinsic magnetic moment associated with electron spin.

14. May 24, 2006

### Gokul43201

Staff Emeritus
To clarify :

A magnetic field does no work on a free charge (the Lorentz force is always normal to the velocity vector).

$$\mathbf{F} = q(\mathbf{v} \times \mathbf{B} )$$

However, a magnetic field will do work on a magnetic moment.

$$U = -\mathbf{\mu} \cdot \mathbf{B}$$

The work is done in rotating the moment to align itself along the direction of the field. The torque felt by the moment is given by

$$\mathbf{\tau} = \mathbf{\mu} \times \mathbf{B}$$

A magnetic moment sitting in a uniform magnetic field feels no net force. However, in a non-uniform magnetic field, it feels a force given by

$$\mathbf{F} = \mu \left( \frac{\partial \mathbf{B}}{\partial z} \right)$$

It is this last force that attracts magnets to each other, or iron filings to a magnet.

15. May 25, 2006

### Mk

Gokul's got some 1337 LaTeX skillz!

16. May 25, 2006

### ptabor

ahhh, thank you Gokul for correcting me. I see it now.