Corresponding to every vector field, there is an associated field of differential 2-forms (the adjoint under stokes theorem). These are basically little weighted planes sitting at every point in space roughly normal to the direction of the current. For these forms there is a clear orientation...
Err, I'm not really sure what you mean by energy deficit. In terms of maxwells equations, the magnitude and direction of the poynting vector is the energy flux. It would always point in the same direction since when E flips, B flips as well keeping the cross product in the same direction.
But that doesn't resolve the issue. Even though you can't achieve perfection, in nearly-destructive configurations there will be less energy stored in the electric field than in nearly-constructive configurations, given the same input laser beam.
Thank you for the response. So then if the heat capacity of the rails is 1 K/J, the rails would in fact heat up by only 81 K, and the other 18 J would go into mechanically changing the momentum of the rails/earth.
I somehow had convinced myself that the work done to change the velocity of the...
I've been thinking a lot about conservation of energy recently, and in addition to my other thread, I have another (quite different) seeming "paradox" that I can't resolve.
Suppose you have a laser shooting into a Michelson interferometer with distances such that the split beam exactly...
I'm having some trouble reconciling the following facts: 1) that kinetic energy depends on v _squared_, 2) at the same time energy is conserved in all reference frames, and 3) reference frames transform linearly in v in classical mechanics (galileo transform). I've basically been able to boil...