# Magnetic force between two parallel straight current wires one of them infinite and the other one finite

This problem is very easy if the magnetic field from the infinite wire is applied over the finite one and the Lorentz force is calculated straightforward.

I'm trying to make the calculation in the other side, I mean, I want to use the magnetic field expression of the field created for the finite wire and to applied it to the infinite wire. In this case, when I try to make the integral for the Lorentz force I obtain a divergent result.

I expect the result would be independent of the magnetic field order used in both calculations.

• A current carrying wire of finite length is by its own a contradiction. It doesn't satisfy the charge continuity equation so Maxwell's equations. May 9, 2021 at 12:36
• If it did exist, the field beyond each end would drop off rapidly, giving a finite force on the long wire. May 9, 2021 at 12:49
• Perhaps I have not well explained my idea. For example in this video F4, force is calculated with the magnetic field expression of the infinite wire and the current I2 in the L side. youtube.com/watch?v=ZECrrEMe3jA Theoretically the result would be the same if the magnetic field expression for the field created by this L finite side is used and applied to the infinite side. But how to do the integration to all the infinite straight wire? May 9, 2021 at 19:24
• In this thread, the calculation is done for two finite straight wires. But how to modify it when one of them is infinite. In the last part of the thread seems that the integral for F12 diverges. physics.stackexchange.com/questions/173035/… May 9, 2021 at 21:58