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Re: [Phys-l] work by magnetic fields



On 4/28/2011 12:13 PM, Philip Keller wrote:
I know I have asked this in the past, but I still don't understand it and my AP students have asked again so...

This is about what some books call a linear motor: a long, u-shaped conducting rail with a conducting bar resting on the rails, free to slide without friction, completing the circuit. There is a battery in the circuit and a magnetic field into the plane of the setup. The battery causes a current to flow and the magnetic field exerts a force on the bar which causes the bar to accelerate (at first -- the induced back emf then causes the current to drop and the bar attains a terminal velocity, but that is not the issue at hand).

The question is: while the bar is accelerating, what force is doing the work that increases the bar's kinetic energy?

Possible answer #1: The magnetic force, F=ILB, that is exerted by the field on the current-carrying bar. That force is in the same direction as the bar's displacement. There is no rule that says magnetic fields can never do work.

Possible answer #2: The magnetic force is not the one that does the work. That force acts on the individual charge carriers in the bar and it is always perpendicular to their motion so it can never do work. But the individual charge carriers are not free to follow the circular orbits that the magnetic field would otherwise cause. They are held by electrostatic forces exerted by the kernels of the lattice atoms. It is that electrostatic force that ultimately does the work.

Any thoughts?
To my mind, this is not a question about linear motors, it a question about why a current carrying straight wire in a magnetic field moves. The Amperes, Biots, Savarts, and Faradays of this world noticed this observable, and formed a relation between the variables.
That is not your issue. You are effectively begging for a relativistic explanation (and there certainly is one) why those slow moving current carriers suffer relativistic effects - why magnetic effects look like electric effects, and so on.

You would probably lose that sense of discomfort, but is it the kind of explanation you would wish on your kids?
Possibly yes, come to think of it - I received just such a throw-away concept while considering undergraduate currents in parallel wires.

Brian W