Paul wrote:
Stephen A. Lawrence wrote:
[snip]
> It's certainly complicated; too complicated to
solve easily
> and too complicated to model mentally with a simple
picture.
Very true! That's why computers are so wonderful.
IMHO the future of science is held
within the computer, as they are great with
mathematics, speed, and memory. Simulations
will break us free from the limitations of the paper
written equations and reveal higher
truths of reality. :-)
[snip]
>>
>> Energy Violation #3:
>> Consider the intrinsic electron spin, which we'll
call
>> ES. Ferromagnetic atoms have unpaired ES, and
therefore create a net
>> appreciable
>> magnetic field outside the atom. Consider two such
atoms that are
>> magnetically
>> unaligned. Now allow the two atoms to align. We
know from atomic scale
>> experimentation from
>> companies such as IBM that during avalanches the
magnetic atoms rotate
>> in magnetic
>> alignment. Typically this can take a few
nanoseconds in
>> non-electrically conductive magnetic
>> materials, and much slower in electrically
conductive magnetic
>> materials (due to
>> eddy currents). Understandably this releases
energy. On a larger
>> scale, if we hold two
>> PM's (Permanent Magnets) that are magnetically
unaligned, we know they
>> want to rotate so
>> they become magnetically aligned. If we allow the
two PM's to rotate
>> they will gain
>> angular kinetic energy as they rotate. In fact, if
there's no friction
>> the two PM's will
>> continue to vibrate back and forth due to momentum
and magnetic
>> attraction. We gain kinetic
>> energy, but also note that the net magnetic field
actually increases
>> as the two PM's
>> rotate and align. According to the above equation,
that also
>> constitutes energy.
>
> Interactions between permanent dipoles are
conservative, as I've
> observed before in this NG. The action of a
magnetic field on a
> permanent dipole can be described with a potential
function.
You left out a world of detail. The net magnetic field
from two nearby ***aligned***
magnetic dipole moments *increases*. The net magnetic
field from two nearby ***opposing***
magnetic dipole moments *decreases*.
I am well aware of that.
Also you need to acknowledge the kinetic energy gained
when two dipoles rotate to align.
Yes, I'm well aware of that.
As I said in my previous message, the action of a permanent magnetic
field on a permanent dipole can be described by a potential function
given by the dot product of the dipole and the field:
-mu <dot> B
(sorry, there's no "\cdot" character in flat Ascii.)
This single function accounts for both linear forces _and_ torques on
the dipole. If you move a permanent dipole around in a fixed (but
spatially varying) magnetic field, the forces and torques it feels are
given by the gradient of the above potential function. The net energy
gained or lost is given by the change in that potential function. When
you return the dipole to its starting position (and orientation) the net
work done will be zero.
Of course, whether both magnets move at once or we nail one down and
allow the other to move, the same thing holds, just as in the case of
two weights connected by a spring it makes no difference whether we move
both at once or just one at a time.
Again, if we replace the magnets with air core
electromagnets then we *CLEARLY* see it
drains energy from the current source.
Yup, the analysis is rather different when we use an electromagnet. In
that case the work done comes from current in the coil.
I did not say this was _simple_. I just said it was conservative.
You need to
ask yourself why two air core
electromagnets that are rotating due to magnetic
attraction gain kinetic energy while
*increasing* the net magnetic field. You need to
understand why that drains energy from
the current source. The answer is simple. It drains
energy from the current source
because there is a gain in KE and net field energy.
Exactly, and if you work out the details it balances.
If we replace the air core
electromagnets with permanent magnets we still gain KE
and an increase in net magnetic
field.
Yes we do. And in this case, as I already said, the action is
conservative; we can't get work out of it.
So you need to ask yourself where that energy
comes from.
I'm well aware of that. But you might just as well say, where does the
energy "come from" when something falls off a table?
In the case of a permanent dipole in a permanent B field, the energy was
apparently there all along, in the form of the -mu*B potential energy
function. If you want to ask more than that, then you're asking why the
electron's B field is quantized, and why its spin can't "slow down", and
there certainly is no simple answer to that. But, lacking evidence to
the contrary, one can take that much of it as a given and go on from
there. Once you've allowed permanent dipoles into the room, the
classical E&M theory can handle them without a problem (only the
assertion that "magnetic fields do no work" must be modified).
I've spent far too much time discussing this with QM
physicists. They have no idea where
the energy comes from once they grasp the issue.
