# Efficiency of induced power

This is a very basic question which I can’t quite wrap my head around. Say you have a wire/coil in a magnetic field in such a way that if you apply a current in the wire it will move. So you charge up a capacitor or some other power source and discharge it through the wire, a force is generated and the wire gets some of that electrical energy converted into kenetic energy via F = BIL.

suppose I have the same charge, same everything but I increase the magnetic field by a factor of 10. The current should remain the same (right?) thus I have increased the force/acceleration by a factor of 10 and thus increased the final speed of the wire also by a factor of 10. Now this doesn’t make any sense, since in theory I could increase the magnetic field strength to some arbitrary number, meaning ”infinite efficiency”, so what am I missing here?

If it’s simply that the magnetic field affects the current, how exactly does it affect the current? (What formulas do I use to calculate the actuall current?)

Thank you in advance for clearing up this confusion in my brain.

• I am not going to try to analyze this whole situation, but you can bet that, yes, some of the energy from the capacitor will be used to produce the kinetic energy. That means the wire will present a back-emf or voltage to the capacitor you're discharging. The electrical power ($IV$) due to this effect will be equal to the mechanical power moving the wire. – The Photon Nov 30 '19 at 1:35