Looks like my "only way to make it work" setup was as you describe, OP, except
that you're making the classic Perpetual Motion Engine errors.
prosilio wrote:The helmholtz magnetic field exerts a lorentz force on the cable and the cable's magnetic field exerts a lorentz force on the coils.
It's easy to say that due to newton's action-reaction principle these forces are cancelled, but are they?
Have you ever made the math?
I did and I don't think cancel each other, unless I'm wrong of course!
Since I can't build a miniature setup to test the above I came here asking you.
So, what do you think?
Ignore exact magnetic field formulae, as they don't add anything at this point.
1) The coils exert a force on the wire can be summarised as FCoilsFieldOnWire + FCoilsFieldOnCoils = 0
, because any force the coil applies on the wire is necessarily balanced by the counter-push back upon the coils.
2) The wire, in turn, exerts a force on the coils that can be summarised as FWireFieldOnCoils + FWireFieldOnWire = 0
, because any force the wire applies on the coils is balanced by the counter-push back upon the wire.
3) It does not matter whether the absolute magnitude of either of the #1 Fs (just concerning the coil-derived lorentz force) matches the absolute magnitude (regardless of sign) of either of the #2 Fs (ditto but the wire-derived component), the force upon the wire is FCoilsFieldOnWire + FWireFieldOnWire
, whether or not the two elements are equal, which you seem to be taking as possible.
4) Ditto FCoilsFieldOnCoils + FWireFieldOnCoils
is the sum total coil-pushing force.
Now add #3 and #4 together, using #1 and #2 statements to simplify the terms. You will
find that it resolves to zero, because #3 is the direct negation of #4. Regardless of whatever differences you perceive (also wrongly, I highly suspect, in this case) between the #1 magnitudes and the #2 ones according to your (mis?)understanding of the coil-lorentz and wire-lorentz equations of force.
If the coil and wire were separate (one on track and one on chassis) the #3 total and the difference (i.e. being the direct negation, so double the 'individual' components) against the #4 total moves the chassis. No problem there. So long as the wire remains in the same position within the coil, which it straight away won't because
of the movement. But you're moving, and if you supply a newly-entering wire(s) further up then you can add more force as required (if you have to, in a system not devoid of friction or if you still need more acceleration). That's essentially a linear motor setup.
But you (definitely, now) have wire mounted on the chassis, along with the coils. The force applied to the coil tries to push the coil pushes the chassis pushes the wire, and the equal-but-opposite force applied to the wire tries to push the wire pushes the chassis pushes the coil in exact opposition
, so nothing at all happens to the chassis+coils+wire that was not already happening to the setup beforehand. Q.E.D.