Mathematical cause of the existence of the remaining resultant internal Lorentz force
19 avril 2012
19 avril 2012
I have
given a rigorous proof of the existence of a remaining resultant Lorentz force
internal to a triangular coil and a numerical computation that confirms this
proof:
Proof of
the remaining resultant Lorentz force internal to a triangular coil
https://docs.google.com/open?id=0B3YDEaOyRUwca0lsRlVfSXpYbWM
https://docs.google.com/open?id=0B3YDEaOyRUwca0lsRlVfSXpYbWM
Why the Lorentz force law cannot respect the
third Newton
I found a compact way of thinking about it. The residual force is due to the asymmetry of one current element acting on the other. For instance, the force of current element 1 acting on current element 2, F12, is not the same as current element 2 acting on element one, F21. If we take the difference we get the following..., (leaving out the denominator for clarity)
ReplyDeletedF = F12-F21 = dI1 x ( dI2 x r ) - dI2 x ( dI1 x r)
= dI1(dI2.r) - dI2(dI1.r)
=r x (dI1 x dI2)
Now the asymmetry in dF is related to the asymmetrical cross product of the
respective current elements. The net force must not be zero since it is an asymmetrical function.
-Dr Jaynes
Your are absolutely correct. This is the origin of the non-respect of the third Newton's law. This is known for long time but physicists love Lorentz so much that they prefer to ignore this violation. They argue that for closed coils the N3 law is respected. The biggest obstacle for me is this wall of denying.
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