# Dynamics of Lorentz force on a current carrying wire

Gold Member
Hello all,

I've been pondering a problem with a current carrying wire in a magnetic field. The Lorentz force is easy, ILB,
with a velocity 90 degrees to the B field. So let the force accelerate the wire. Assume only one segment of the wire that has current in one direction, say up, is in the field and the field is out of the page (screen!). The force is to the left. It now moves. For a fixed current, the force should be constant and thus the acceleration.

Now, let's look at it from a reference frame co-moving with the wire. At some instant we see an electric field pointing down, against the current flow according to how fields transform. The magnetic field is virtually the same for low velocity. It's clear that to maintain the acceleration we must maintain the current and to do that we must overcome the increasing electric field opposing the current flow.

First, is this correct? Second, does the electric field have to oppose the current? Does a current carrying wire immersed into an electric field have to be affected since conductors usually keep external fields out?

I'm bothered by the idea that if I found myself in a infinite uniform magentic field in space from an unknown source, why should I be able to compute my relative speed to it just by turning on a current in a wire? If the universe was filled with a uniform magnetic field, we could always know our velocity which seems wrong. I'm also bothered by the fact that I shouldn't have to transform into the moving frame to know what happens. I should be able to know all by staying in the original reference frame. Thanks.

tech99
Gold Member
.
Isn't the opposing electric field the back-EMF experienced by all motors due to generator action?
The source of current must overcome this BEMF and must do work to provide KE for the moving wire.
Regarding the question about finding velocity in the Universe, I think you could find your velocity relative to the magnetic source.

Gold Member
Isn't the opposing electric field the back-EMF experienced by all motors due to generator action?
The source of current must overcome this BEMF and must do work to provide KE for the moving wire.
Regarding the question about finding velocity in the Universe, I think you could find your velocity relative to the magnetic source.

Thanks. Back emf is usually attributed to Lenz's law which is dependent on changing magnetic flux. In my scenario, the flux is constant (or so I think it is). It should be possible to evaluate what will happen from the original frame. For instance, if the flux changed with the observed velocity that would be the case. Also, if an electric charge is accelerated by a constant electric field parallel to its motion, there appears that no such counter effects which will slow it down such as a relativistic transformation that provides a counter force. Interesting the magnetic case is not symmetric.

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