# Lorentz-contracted Current

Q:
How does a wire stay neutral to an outside stationary observer if it has an electric current flowing through it which is contracted by length contraction according to Special Relativity?
- Tausif Hossain (age 18)
A:

I'm not sure what you mean by a "stationary observer". Let's say you mean an observer who is stationary with respect to the center of mass of the entire circuit. The density of the electrons in that frame can still be uniform. Now let's switch to a different frame, moving with respect to that. The Lorentz contractions of the negative electrons and the positive nuclei will differ in that frame because of their different velocities. That mean that in this other frame the wire will not be neutral. Parts of the circuit will look positively charged and other parts will look negatively charged, because the current is flowing around in a loop.That means that a charged particle at rest in this frame (moving in the original center-of-mass frame) will see an electric field and accelerate.

How would an observer using the original frame describe the acceleration of that particle, which he describes as moving? He must say that the current in the wire produces forces on moving particles. Those forces are called "magnetic", specifically the "Lorentz force".

You may find a beautiful description of this logic in Purcell's book on Electricity and Magnetism.

Mike W.

(published on 06/12/2017)

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