George Holz wrote:
Stephen A. Lawrence wrote:
What's more, a magnetic field _does_ _no_ _work_, _ever_. It's
typically hard to see exactly what's really happening with a permanent
magnet, but this law is always followed: the force exerted by a
magnetic field on a charged particle is always perpendicular to its
motion, and hence cannot impart energy to it.
As to a citation, check any E&M text. The "standard" reference on this
is probably Jackson, titled something like "Electrodynamics".
Griffiths' text on the same subject, "Intro to Electrodynamics", is
generally considered more accessible, however.
Yes , I have both of these books and have noticed the " magnetic field
does no work" line in Griffiths and other texts. This is the interpretation
in all texts that I have seen. I find that this statement is somewhat
misleading and most students probably find it confusing as the
interaction of two magnets can obviously do work. Force * distance is
work.
What is being done here is a somewhat arbitrary classification of
electromagnetic forces into electric and magnetic forces. The Lorentz
force law F=q(E+VxB) actually hides what I think of as a
longitudinal magnetic force included in the original Ampere law
inside the qE term. The earlier Ampere law included this interaction
between the magnetic fields of moving charges as an explicit term.
A straight forward application of the Lorentz law gives the same total
force of a magnetic field on current flow around a complete circuit as the
Ampere law but not the correct distribution of forces along the wire.
This has been shown in many experiments including my own but is
largely ignored in texts. Tom Phipps has written about the problems
with the Lorentz force law in Infinite Energy and in his book
"Heretical Verities". He and others have suggested adding a longitudinal
term which provides invariance and matches experiment.
If you want to look at a far, far simpler case which can be understood
without knowing how magnetic domains work, take a look at my "A little
brain teaser" post from last night. It's a tightly constrained gedanken
experiment in which the rules of the game guarantee that the B field
does no work, yet it shows the same "Darn the magnet obviously just
performed work!!" effect. In that case, it's obvious where the energy
comes from, though. I posted it as a "puzzle", and I didn't originally
intend to post the solution for a day or two, but that plan no longer
looks so hot, so I'll just say that in the gedanken experiment the
spinning ring slows down. Total energy of the system -- rotational
energy + linear kinetic energy -- must be conserved, and the right-hand
rule quickly leads to the conclusion that as the ring moves through the
field toward the box it experiences a torque opposite its direction of spin.
Yes the ring slows down, but the dipole field also provides energy.
How does the spin of the ring slow down? The only force that will slow the ring
must be longitudinal to the electron motion.
<g>
No, it's not -- not in the "stationary" frame!
The ring moves _sideways_ through the field as it spins. While it's
sliding sideways the direction of motion of the charges on the ring is
no longer purely tangential to the ring, and the Lorentz force -- which
is perpendicular to the line of motion -- is consequently not purely
radial. It has a tangential component.
The thing you need to keep firmly in mind is that all motions considered
here are as seen by an observer stationary in the "laboratory frame" and
in that frame the motion of the charges is not simple rotation about the
ring's axis; it's got a translation added to it. The charges are
following something more akin to a cycloidal path than a circular path.
Here's a picture which may help; the red line, motion of the charges, is
supposed to be the sum of the green line (translation) and the black
curve (rotational velocity) (ok ok the lines are not drawn not to scale,
sorry):
http://www.physicsinsights.net/images/moving-ring.png
The B field is assumed to point UP through the page, so the Lorentz
force lies in the page and is perpendicular to the net motion of the
charges.
If, instead, you want to view it from the POV of an observer riding on
the ring, or from the POV of an observer fixed at the center of the
ring, then your POV is no longer stationary with respect to the
laboratory. In that case, when you transform the B field to your new
frame of reference you find that there's an E field present as well, and
that's the culprit "doing the work".
If you want to save the Lorentz force law you will have to include dynamic
electric fields along the ring caused by movement through the changing magnetic
fields.
Again, I only need to do that _if_ I want to view the problem from a
frame moving with the ring, and in that case the Lorentz transform of
the B field provides me with the needed E field. If I stick with the
frame of reference which is stationary with respect to the table (and
the black box) then the only forces come from the VxB component, and
that's all that is needed ... but again, in that case the ring is
translating and V isn't purely tangential, and there is a component of
VxB which _is_ tangential.
Think of it as
being caused by voltage induced by magnetic induction.
In general when magnets are attracted to each other and move closer,
total field energy increases and the energy comes from the individual
dipoles. That would be the electron spin and orbital motion dipoles.
George Holz
Varitronics Systems
