TITLE: Deflection the needle of moving compass by magnetic field
QUESTION [3 upvotes]: I have a question about electromagnetism. Probably I understand something in a wrong way. So, I know that the drift velocity
 of electrons in conductors is very small ($\sim$ $0.1$-$1$ mm / s). Also I know that if I put the compass to the wire, the needle is deflected. 
Suppose I've started moving compass along wire with drift velocity. Is there deflection of neadle in this case?

REPLY [2 votes]: Just for the record, and this is really just a reprise of Jonas' answer and the comments:

a current flowing and the compass is stationary:
in the rest frame of the compass there is a flow of negative charge and this generates the magnetic field.
a current flowing and the compass is moving at the electron drift velocity:
in the rest frame of the compass the (conduction) electrons are stationary but there is a flow of positive charge in the other direction and this generates the same magnetic field.
a current flowing and the compass is moving at some velocity in between zero and the electron drift velocity:
in the rest frame of the compass there is a flow of negative charge in one direction and a flow of positive charge in the other direction and the two flows generate the same magnetic field.

So whether the compass is stationary, moving at the drift velocity or any velocity in between, the deflection of the compass is the same.
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