Can a magnetic field do work on a current-carrying piece of wire?

In summary: AC voltage across the coil is changing with time, and this change in voltage is converted to direct current by the field coil).
  • #1
epsilonjon
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0
[PLAIN]http://img826.imageshack.us/img826/2928/19002018.jpg [Broken]

Suppose I have a slidewire generator as in the image above.

If I move the sliding rod to the right I generate a current in the loop, directed anticlockwise. It takes work to move the rod, since the induced current is interacting with the magnetic field and experiencing a force to the left. The rate at which work is done by the applied force is equal to the rate of energy dissipation in the circuit, since you can't violate energy conservation.

Is it not the case here that the magnetic force is doing (negative) work on the current-carrying rod as it moves? I do not understand this, as the magnetic force on a moving charge is always perpendicular to its velocity, and so can never do work.

This caused me to go over the derivation of the [tex]\vec{F}=I\vec{L}\times\vec{B}[/tex] equation for the force on a current-carrying wire in a magnetic field. The few books I have all use the same sort of method, whereby they take the magnetic force on an electron at some instant then multiply it by the total number of electrons in the wire. Now I am thinking how can this be correct, as they're implying that the force on the electrons in the wire will always be in this same initial direction, contradicting what they've said earlier about moving charges in a magnetic field undergoing circular motion?

If someone could straighten this all out for me I would really appreciate it, as I don't want to keep reading before I understand this properly.

Many thanks!
Jon.
 
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  • #2
epsilonjon said:
[PLAIN]http://img826.imageshack.us/img826/2928/19002018.jpg [Broken]

Suppose I have a slidewire generator as in the image above.

If I move the sliding rod to the right I generate a current in the loop, directed anticlockwise. It takes work to move the rod, since the induced current is interacting with the magnetic field and experiencing a force to the left. The rate at which work is done by the applied force is equal to the rate of energy dissipation in the circuit, since you can't violate energy conservation.

Is it not the case here that the magnetic force is doing (negative) work on the current-carrying rod as it moves? I do not understand this, as the magnetic force on a moving charge is always perpendicular to its velocity, and so can never do work, or in your case negative work.

This caused me to go over the derivation of the [tex]\vec{F}=I\vec{L}\times\vec{B}[/tex] equation for the force on a current-carrying wire in a magnetic field. The few books I have all use the same sort of method, whereby they take the magnetic force on an electron at some instant then multiply it by the total number of electrons in the wire. Now I am thinking how can this be correct, as they're implying that the force on the electrons in the wire will always be in this same initial direction, contradicting what they've said earlier about moving charges in a magnetic field undergoing circular motion?

If someone could straighten this all out for me I would really appreciate it, as I don't want to keep reading before I understand this properly.

Many thanks!
Jon.

Only free charges move in circular orbits when traveling with velocity in a constant magnetic field. Free particles travel in straight lines unless acted on by a force. In this example the only force is the Lorentz force which is unable to add kinetic energy to the particle. Also, there is no change in potential energy when a particle moves in a constant magnetic field, so there can be no net change in energy for the particle.

A current is an example of charges moving under the force of an electric field, so the above does not apply. Even in your example, the magnetic field is not doing work because it is constant. Instead the voltage times current is the power that is doing the work.

However, this whole business of "the magnetic field doing no work" is a misleading statement because clearly magnetic fields can do work. If you bring two magnets together, work is done. Two parallel conducting wires can also do work. It's really only constant magnetic fields that do no work. This should make sense because the magnetic field has energy, and if it is constant, then its energy is constant and no work can be done by it.
 
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  • #3
This has been covered exhaustively in other threads, but no, magnetic fields cannot do work on charges. Note that two magnetic fields (from magnets) forming say a repulsive arrangement is really the same as the force between two current-carrying wires. And the work done by pulling the wires apart is done against the electric field forcing the current, not the magnetic field. (this is how a generator works, and it's also why no power is delivered to the field coil of a generator. All the power comes from the shaft rotation. Big hydro generators for example don't use permanent magnets, they use field windings to create the magnetic field. The only power delivered to them is that needed to overcome resistance losses. The magnetic field of the field coil does no work.)
 
  • #4
I agree with the above comments related to motors and the OPs example, however, I'd like to make some comments and clarifications to indicate what I was trying to say above. Note that I clearly stated that the OPs examples were not a case of magnetic fields doing work.

Antiphon said:
This has been covered exhaustively in other threads ...

Precisely because blanket generalizations cause confusion and require clarification.
Antiphon said:
, but no, magnetic fields cannot do work on charges.

This is an example of a blanket statement that is usually true, but is misleading because counter examples can be found, unless extra conditions are added.

For example, take a charge of arbitrary shape and spin it. This charge will now have a magnetic moment that can interact with a nonuniform magnetic field, and the magnetic field can do work in this case.

Antiphon said:
Note that two magnetic fields (from magnets) forming say a repulsive arrangement is really the same as the force between two current-carrying wires. And the work done by pulling the wires apart is done against the electric field forcing the current, not the magnetic field.

Some might say that magnets and current carrying wires are not really the same, but let's assume they are the same. Two magnets can certainly do work, and yet, where is the electric field you are speaking of in this case? Assume we are working in the obvious stationary frame of reference.

The issue here is that a magnetic field can store energy, and that potential energy can be used to do work. Granted, the case of magnets (or wires) attracting is a dead end process because the stored energy is used up, and work would need to be done to separate them again. However, it would be incorrect to say that no work has been done when two magnets are brought together. For example, two magnets could be oriented in an attractive position in a tube with a spring between them. The spring would then compress and the magnets would move closer together. Here, the potential energy of the magnetic fields is converted into potential energy in the spring. Also, two magnets can be oriented in a repulsive arrangement in a tube, and this can act as a spring, all by itself. Energy can be stored and released by doing work with, or having work done on the magnetic spring.

So the more general statement you sometimes hear ("magnetic fields do no work") is even more misleading than the statement that "magnetic fields do no work on charges", since it is akin to saying that springs do no work.
 
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  • #5
Stevenb, thank you for taking the time to write a thorough answer - i definitely think i understand it better now.

If you don't mind I also have one more question... A changing magnetic flux through a conducting loop causes an emf to be induced in that loop, right? So say I have a little solenoid with a time-varying current going through it, producing a changing magnetic field, and I put this at the centre of a huge circlular loop, say 1 light-year across. There is a changing magnetic flux through the loop, so this still induces an emf in it, even though the cause and effect are so far apart? I do not understand how this could occur! :bugeye:

P.S. sorry if this has been covered elsewhere, but i did do a search and couldn't find anything.

Many thanks,
Jon.
 
  • #6
epsilonjon said:
Stevenb, thank you for taking the time to write a thorough answer - i definitely think i understand it better now.

If you don't mind I also have one more question... A changing magnetic flux through a conducting loop causes an emf to be induced in that loop, right? So say I have a little solenoid with a time-varying current going through it, producing a changing magnetic field, and I put this at the centre of a huge circlular loop, say 1 light-year across. There is a changing magnetic flux through the loop, so this still induces an emf in it, even though the cause and effect are so far apart? I do not understand how this could occur! :bugeye:

P.S. sorry if this has been covered elsewhere, but i did do a search and couldn't find anything.

Many thanks,
Jon.

Well, that is certainly a very good question, and is one I recall thinking of many years ago. I'm struggling to find a nice clean and simple explanation, so I'll think about it more, and perhaps expand on my answer later. However, I can get you thinking about this as follows.

One issue is your qualification that you have a "little" solenoid. If the solenoid is little, then the flux lines are going to circle back within your 1 light year loop. Hence, the net flux change will effectively be zero. It's actually very difficult to keep the leakage flux from coming back within even a small loop.

Now, what if we expand your question to a large scale (thin and very long, let's say 10 light years long) solenoid? Indeed, your question becomes a nice thought experiment. But, now consider your assumptions and think about how you would drive current into a 10 light year long solenoid. You now have a challenging field problem to solve because the electric current and electric fields for the solenoid are not instantaneous, as usually assumed in a table-top experiment. In the end, the solution for this problem will involve retardation effects and electromagnetic wave propagation. Not a trivial problem to solve and requires more than just Faraday's Law to do correctly.
 
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  • #7
  • #8
stevenb said:
Now, what if we expand your question to a large scale (thin and very long, let's say 10 light years long) solenoid? Indeed, your question becomes a nice thought experiment. But, now consider your assumptions and think about how you would drive current into a 10 light year long solenoid. You now have a challenging field problem to solve because the electric current and electric fields for the solenoid are not instantaneous, as usually assumed in a table-top experiment.
Yeah I see now it's not as simple as just "put a little solenoid in it the middle and you get a flux" :p

To be honest I'm just starting to learn the basic physics behind inductors as I'm self-teaching myself a bit of electronics. I won't think too much more about this problem as I keep getting bogged down with little details. It's been about 3 weeks and I haven't even gotten to the section on R-L circuits yet! :tongue:

Cheers, Jon.
 
  • #9
stevenb said:
Only free charges move in circular orbits when traveling with velocity in a constant magnetic field. Free particles travel in straight lines unless acted on by a force. In this example the only force is the Lorentz force which is unable to add kinetic energy to the particle. Also, there is no change in potential energy when a particle moves in a constant magnetic field, so there can be no net change in energy for the particle.

A current is an example of charges moving under the force of an electric field, so the above does not apply. Even in your example, the magnetic field is not doing work because it is constant. Instead the voltage times current is the power that is doing the work.

So, the magnetic forces generated in a motor by the magnetic fields is not doing work? But its the total input of the electrical energy?

What if the magnetic field was not contant but changing in time. Would the total force on the current change? Its confusing to me... Without the magnetic fields no force can be generated and no "torque" is created by the force... Based on Lorentz law : F = IL x B , its seem as if magnetic fields can do work on a wire carrying current in a 90 degree axial. Magnetic fields can never do work on electric charges?

https://www.physicsforums.com/showthread.php?p=3996836#post3996836

Post you're answers here please.
 
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1. How does a magnetic field do work on a current-carrying piece of wire?

A magnetic field can do work on a current-carrying piece of wire by exerting a force on the moving charges within the wire. This force causes the charges to move, creating an electrical current.

2. Can a magnetic field change the direction of a current in a wire?

Yes, a magnetic field can change the direction of a current in a wire by exerting a force on the moving charges within the wire. This force can cause the charges to change direction and therefore change the direction of the current.

3. How does the strength of a magnetic field affect the work it can do on a current-carrying wire?

The strength of a magnetic field is directly proportional to the amount of work it can do on a current-carrying wire. A stronger magnetic field will exert a greater force on the charges in the wire, allowing it to do more work.

4. Can a magnetic field do work on a stationary wire?

No, a magnetic field can only do work on a current-carrying wire when the charges within the wire are in motion. If the wire is stationary, there is no current and therefore no work can be done by the magnetic field.

5. How is the direction of the force exerted by a magnetic field on a current-carrying wire determined?

The direction of the force exerted by a magnetic field on a current-carrying wire is determined by the right-hand rule. If the thumb of your right hand points in the direction of the current, the fingers will curl in the direction of the force exerted by the magnetic field.

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