# Special relativity when observer is traveling with the electrons creating current

There was a situation that has completely baffled me.

  I<--
-----wire-----

q


Essentially there are 3 things going on.

1. Positive Charge: Below the wire (on the page) moving to the right with speed v
2. Current Carrying Wire: Above the positive charge. Current points left because electrons within wire are moving to the right with speed v.
3. The observer of all of this is also moving to the right with speed v.

So in summary there is an observer, a positive particle, and electrons in a current carrying wire all traveling to the right with the same velocity.

The goal is to determine the forces on q whether they be electric or magnetic.

I got this problem completely wrong so here are some assumptions I made to get to my solution. One of these must be incorrect.

1. While to the observer the electrons inside of the wire are now stationary the protons that are in earth reference frame stationary appear move left with velocity v now. Thus the observed current seems to have the same magnitude and still points in the same direction.
2. Due to this observed current there will be a magnetic field going around the wire. Same direction as it did with it stationary. So the electron would feel a magnetic field out of the page.
3. In the reference frame to the observer the particle however has no velocity. Therefore there cant be any magnetic force on the particle.
4. Current carrying wires don't create electric fields.

Therefore I concluded that there are no forces on the particle in the particles reference frame.

This is incorrect.

The answer claims that there is an electric force going down the page.

What am I misunderstanding here?

• Just remember that there is no experiment an observer can do that will tell him if he is moving or standing still. in his reference frame all will work the same as if he were standing still. – Adrian Howard Jun 13 at 9:09