I Does Moving a Wire Increase its Magnetic Field?

[jamesconnolly81]

Folks,

I'm not sure if this is the correct forum topic for my question, but it seems to be close or related.

Question: If you have a wire carrying current then it creates a magnetic field as in the diagram in the link below.
https://nationalmaglab.org/educatio...ay/interactive/magnetic-field-around-a-wire-i
The electrons are moving upwards. What happens if you then move the wire itself upward at a constant speed ?
Does that in any way add to or help the current in any way ? In other words does the magnetic field increase when measured at a fixed point ?

Thanks James

 

[vanhees71]

You find the fully relativistic solution for the wire at rest here:

https://www.physicsforums.com/insights/relativistic-treatment-of-the-dc-conducting-straight-wire/
Now just Lorentz boost all the quantities (in my notation in $z$ direction).

 

[Dale]

Does that in any way add to or help the current in any way ? In other words does the magnetic field increase when measured at a fixed point ?

@vanhees71 gave the mathematical answer, so I will add a qualitative answer. Around an uncharged current-carrying wire we have no E field and the B field is in the plane perpendicular to the wire.

You can use the equations in this link to determine the fields in a frame where the wire is moving: https://en.m.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

Briefly, you get an E-field pointing radially outward from the wire and the B field increases by the usual Lorentz factor.

 

[vanhees71]

But in the rest frame of the wire you have a transverse E-field (in addition to the E-field along the wire keeping the current flowing), and the wire is not uncharged! That's the important point of the above quoted Insights article. Amazingly the relativistic treatment of the current-conducting wire is wrong in many textbook by just assuming that the wire is uncharged in the wire restframe, which however is wrong due to the correct relativistic version of Ohm's Law. As shown in the Insights article (and the nice paper quoted in there), the wire is uncharged in the rest frame of the conduction electrons. All this is easily understood as a consequence of the "self-induced Hall effect" on the current.