Paul wrote:
Stephen A. Lawrence wrote:
[snip]
>> You mean sci.physics.relativity.pub? I'd like to
know
>> where physicists such as Ed Witten hang out
online. :-)
>
> The news group "sci.physics.relativity". It's
crawling with total
> loonytunes with just a few real physicists. Ed
Witton doesn't sound
> familiar; I don't think he hangs out there
(probably has more sense).
Well you should recognize the name Ed Witten. He's
the guy who took all the nightmarish
flavors of the superstring theories and created
M-theory! :-) He's almost worshipped in
the physics community.
[snip]
>> Yes, understandably, but I'm just trying to come
up
>> with ideas to meet the demands of conservation of
energy. I'm sure
>> there must be some
>> genius QM physicists out there that have an
answer. So far haven't
>> met any with an
>> answer, but I would expect some silly answer such
as, "Oh yeah, the
>> energy comes at the cost
>> of information. The probability of knowing the
electrons location
>> decreases." ;-)
>
> Actually as I think about this it seems like the
overall field strength
> and, hence, field energy must decrease as two
dipoles approach (due to
> the fields of the two dipoles "mostly canceling").
I don't know if the
> reduction in field energy matches the gain in
mechanical energy but it
> might.
No, no, no. Two magnetically aligned dipoles increase
the net magnetic field.
That's true, but two aligned dipoles don't attract each other.
You need to flip one so they're N-S, S-N for there to be attraction, and
in that case the fields cancel as they approach. If they're identical
(but with one flipped), and if you could move them together until they
were co-located, you'd have zero net field.
Here's a picture of two dipoles, oriented vertically, which will attract
each other (using coils produces the same result but is harder to draw
in flat Ascii than the "mythical" two-charge dipoles):
N S
| |
| |
| |
S N
When they are allowed to go all the way together, so that they're
touching, the colocated N and S "charges" produce canceling fields:
NS
||
||
||
||
SN
With two _aligned_ dipoles, on the other hand, they repel; you need to
do work on them to force them together. And then, the fields add, and
since the energy in the field goes as the square of the strength, you
end up with double the total field energy you had to start with (or
something close to it) as the energy density quadruples (square of field
strength, of course) and the volume filled by the two fields drops by
half. Two repelling dipoles:
N N
| |
| |
| |
S S
If we force them against each other, they're oriented such that their
fields will reinforce:
NN
||
||
||
||
SS
> That, on the other hand, leads to problems in the
case with two
> electromagnets, where the same reduction in total
field strength must
> occur, _but_ where we've already paid the energy
bill by overcoming the
> back EMF in the coil as it moves through the
field....
Again, you have it backwards. See above comment.
I think I have this straight, but I may have said it wrong.
If we place two relatively INVERTED electromagnets next to each other,
they attract each other, and if we allow them to come together, there's
a back EMF as they approach, and we need to add electrical energy to
maintain the current in the loops. If we have two ALIGNED
electromagnets, to bring them together, we need to _force_ them together
(they repel) and as we do so, there's an induced forward EMF -- we get
electrical energy out. If we get mechanical work out, we need to put
electrical energy in, and conversely.
The case with electromagnets is confusing, unfortunately, because the
field is more complicated than with infinitesimal permanent dipoles --
for a counterclockwise current, the field goes "up" inside the loop and
"down" outside the loop; when we shut off the current it's the field
_inside_ the loop that gives back its energy to the loop, via
del x E = -dB/dt
When dB/dt points "up" (increasing field strength), curl(E) points down,
and the induced EMF is clockwise (which is reverse the direction of
current flow).
But unless the loops actually overlap physically, the "external" field
of one loop is superimposed on the "internal" field of the other loop;
hence, with two relatively inverted loops, within each loop the field is
reinforced rather than canceled by the presence of the other loop. The
extra energy in the fields, which you _can_ recover (by opening both
loops simultaneously), comes from the fact that it actually takes twice
as much electrical energy to power the loops while they pull themselves
together as you recover in mechanical energy. Conversely, you get out
twice as much electrical energy out as the mechanical energy you put in
when you force aligned loops together; the extra energy comes from the
lost field energy within the current loops (which is no longer
recoverable by opening the loops, and so is a "real" loss).
Regards,
Paul Lowrance
