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Science Forum Index » Physics - Electromagnetic Forum » Paradox? Net force on L-wire section fed current by...
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| Neil B.... |
 Posted: Sat Jun 07, 2008 9:00 pm |
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Guest
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It should be fun and maybe illuminating to play with the following
paradoxes (the second in a different post.) They'd be a good thing
to write up in American Journal of Physics (maybe I'll try) if not
already. I wrote about them some years ago but never saw examples
from anyone else.
LMK if you've heard of things like the following anywhere, tx.
Magnetic interactions produce a net force when current runs through an
L-shaped wire section. We usually think about complete circuits (due to
their greater usefulness) but of course current can run from a charge
reservoir, through a section of wire to another reservoir (receptacle.)
Capacitors are just one example. Have a reservoir at one end of a wire
"L", and let current run through to the receptacle at the other end until
exhausted. The changing charge adds additional magnetic field
(rationalized units: Curl B = J + at (no spam) E/ at (no spam) t) to the Amperian component from
current, but it's the same sort of circular fields in the same
orientation. The forces on the current sections are as I dL cross B, so
the forces between wires are perpendicular to the wires. They don't cancel
out because the wires aren't parallel. The L-wire should get a push, an
impulse f Delta t. Note that in principle, we could such charge into the
receptacle end, then send current back the other way around to the former
reservoir. The net force is in the same direction, so we can keep pushing
the L along. Furthermore, the faster the current flows, the bigger the
total impulse since force is propl. to I^2 and Delta t propl. to 1/I.
That may seem like no big deal if you've heard of momentum and energy
being stored in fields, and maybe, ultimately, it isn't. However, there
are some odd features of this. For one, the field produced is partly from
accelerating charges, but isn't "radiation" in the conventional sense as
from a photon rocket. For one thing, it isn't a thrust in a given
direction (well, clearly directed) and doesn't have a particular
frequency. In order to get relations to work right for photon propulsion,
don't we need to get a particular red shift of the thrust pushing the
rocket, so the increase in rocket momentum and energy is balanced by a
loss of those quantities in the photon stream? Also, note that the thinner
we make the wire, given a nice square corner, we can increase net force
without limit (in principle) since the B around a long wire section
("semi-infinite" approximation) goes as 1/r, which gives integral = ln b -
ln a. Of course the fields get stronger as well, but it seems odd we can
get so much push out of this construction. It sure does *look* like
reactionless drive. What "pays" for it and how?
Working on things like this stirs up insight and less stale thinking about
EM fields, since it seems not to be one of the cliché problem examples. In
any case, a cute unusual way to get propulsion. |
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