Interactions of Moving Particles: Magnetic Fields and Experimental Results

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Lets say we have two muons (or electrons, protons or larger bodies, etc) moving in the same direction with the same speed. If stationary they will repulse each other. If in motion to a stationary observer they will create and interact by the magnetic field around them, pulling toward each other. What the observer will see if travel at the same speed, and direction with the particles ? Repulsion or attraction? What is the laboratory experiment result ?


Another one is, if a magnetic compass will show any magnetic field around a straight wire with a dc current in it, if the compass is moving along the wire, same direction with the speed of the electrons, (a few mm/sec) ?
I know that this is an old question but i just can't find a satisfying answer...thanks!
 
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The electric repulsion is always greater than the magnetic attraction for this case.
The electron drift velocity in a wire is very small. Moving a compass at that rate will have a negligible effect. The magnetic field of the wire is caused by the difference in motion of the electrons and the positive charge. This will not change by a slow motion of the compass.
 

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