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

Thread Starter

epsilonjon

Joined Feb 15, 2011
65
Hi.

I understand that, with an electron moving perpendicular to a magnetic field, the Lorentz force acting on it will be perpendicular to both the velocity vector and the magnetic field. Hence the force cannot change the magnitude of the velocity, only its direction, and the electron moves in a circular path.

But then later in my book it moves on to discuss the force on a current-carrying piece of wire due to a magnetic field. I follow the derivation of this force, and it ends up with \(\vec{F}=I\vec{L}\times\vec{B}\). I thought I understood this okay, but then after more thought something is puzzling me. Imagine I have some space with a B field constant over it, and into this I put a straight piece of wire of mass m, carrying constant current I perpendicular to the B field. The above force will act upon the wire and accelerate it, as a whole, in a direction perpendicular to the current and the B field. So is it not the case here that the B field is doing work on the wire?

Can someone please help me to understand this, as the conclusions of the above paragraphs seem conflicting. :confused:

Many thanks!
Jon.
 

t_n_k

Joined Mar 6, 2009
5,455
Electric motors work on this principle. Electrical energy (work) is transferred between a stationary and moving component via a magnetic field to produce mechanical output energy.
 

Thread Starter

epsilonjon

Joined Feb 15, 2011
65
I think you misunderstand my question.

If the magnetic field cannot do work on a charged particle, then how can it be doing work on the wire?
 

t_n_k

Joined Mar 6, 2009
5,455
Perhaps it has something to do with the interaction between magnetic fields rather than between magnetic field and charge(s). It's a moot point.
 

t_n_k

Joined Mar 6, 2009
5,455
To take up your thought experiment on the piece of current carrying wire in a uniform orthogonal magnetic field.....

So the wire has current which presumably has come from an electrical energy 'source'. As the conductor accelerates in the field it will generate an emf in relation to its motion in the field. This emf will oppose the energy delivery from the source. If the source is a voltage source, its emf would eventually be just balanced by the induced emf at some wire velocity and no further acceleration would be possible as the current would have fallen to zero. No further energy is delivered to the wire system and it continues at uniform velocity 'ad-infinitum'.

For work to be done then there must be some energy input to the system.

In the case of the electron entering a uniform magnetic field at some initial velocity there is no means by which additional energy can be provided to the electron - it simply deviates along a circular trajectory. Is it possible that this electron can emit energy as radiation - it is being accelerated towards some notional central point of its trajectory? If it emits energy will it possibly begin to spiral inwards???
 
Last edited:

BillO

Joined Nov 24, 2008
999
In the first case, the electron in the magnetic field, the electron is being accelerated. A force is acting on it to move it in a circular path. Work is being done, but not by the field. The work is being done by the kinetic energy the electron has. It will eventually slow down. Energy will be lost both to radiation (as per TNK) and to acceleration of the electron into a circular path.

In the second case the work is being done by whatever is supplying the current to the wire.


In either case, the constant, all pervasive magnetic field is doing no work.
 

shortbus

Joined Sep 30, 2009
10,044
Don't remember what the circuit is called, but some welders use a Dc coil over top of an AC transformer to control the current in the transformer. Isn't that using a magnetic field to limit the flow of another electric force?
 

t_n_k

Joined Mar 6, 2009
5,455
Don't remember what the circuit is called, but some welders use a Dc coil over top of an AC transformer to control the current in the transformer. Isn't that using a magnetic field to limit the flow of another electric force?
You are probably thinking of a "saturable reactor".
 
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