While chatting with a friend, I came up with something to think about, being, "if two parallel wires, with constant and equal current wrt position, are put next to each other, the charges in the wires can exert normal forces on the wires, and they're left at rest wrt one another to interact freely, what will happen from the point of view of the initial rest frame of the wires?"
After a bit of RHR'ing, it turns out each wire feels a force away from the other. My friend and I having a dispute over if the current decreases.
(EDIT: A bit more RHR tells me they attract, not repel.)
I'm stating, well, two things. The first feels somewhat deprecated due to the fact that a particle with velocity u+v doesn't have kinetic energy equal to (the kinetic energy of a particle with velocity u + the kinetic energy of a particle with velocity v,) but hopefully the underlying point is still valid.
Argument 1: As the wires accelerate away from each other, they gain kinetic energy. This obviously has to come from somewhere, and the logical place for it to come from is the motion of the charges along the wire. Thus current decreases.
Argument 2: Using something like Euler's Method, after a short amount of time, the charges will have some of their velocity directed away from the other wire, and thus, assuming all components are real, less of their velocity will be directed along the wire. (Magnetic fields don't really do any work on particles.) Thus, as current is related to the component of velocity along the wire, current decreases.
After a bit of RHR'ing, it turns out each wire feels a force away from the other. My friend and I having a dispute over if the current decreases.
(EDIT: A bit more RHR tells me they attract, not repel.)
I'm stating, well, two things. The first feels somewhat deprecated due to the fact that a particle with velocity u+v doesn't have kinetic energy equal to (the kinetic energy of a particle with velocity u + the kinetic energy of a particle with velocity v,) but hopefully the underlying point is still valid.
Argument 1: As the wires accelerate away from each other, they gain kinetic energy. This obviously has to come from somewhere, and the logical place for it to come from is the motion of the charges along the wire. Thus current decreases.
Argument 2: Using something like Euler's Method, after a short amount of time, the charges will have some of their velocity directed away from the other wire, and thus, assuming all components are real, less of their velocity will be directed along the wire. (Magnetic fields don't really do any work on particles.) Thus, as current is related to the component of velocity along the wire, current decreases.