# Conservation of Energy on Current-Carrying Wire in Magnetic Field

yosimba2000
So force on a current carrying wire = ILxB.

If I have a bunch of bar magnets making a uniform magnetic field of strength B, then a 1 meter long wire of 0 ohms carrying 1 Amp, the force on that wire is (1)(1)xB = 1B. If I let that force move the wire for a time T, let's assume the wire moved a distance X. So the work done on the wire is 1BX joules.

Now let's say I keep everything the same but double the magnetic field using stronger magnets. So now Force on this wire is (1)(1)(2B) = 2B. Since the force is double the original and acting on the same object, if I let it act upon the wire for the same amount of time T, the wire will move a longer distance than the original X, let's say 1.5X. So the work done on this wire is (2B)(1.5X) = 3BX joules.

My electrical energy input was the same in both scenarios: E = IVT. I, V, and T were the same in both experiments, but the energy exerted on the wires were different by a factor of 3. How? I understand the force is larger, but how did I get 1BX and 3BX joules of energy for the same electrical input? It must have come from somewhere, but where? It's not as though the magnets "lost" magnetic energy and became less magnetic.

I suggest you can try to describe your system with differential equations. • 