Moving charge as a magnet, is the sign relative?

Question

A thought experiment:

Suppose we are moving in a spacecraft (A), carrying an excess of electrons on spaceship surface, but we can't go outside to measure it, and it's moving at constant speed $v$, with respect to other distant ship (B).

When (A) pass in front of the ship (B), suddenly the two metal ships start to approach at increasing speeds, it's because of the force from magnetic field generated by the relative speed of moving charges .

We have to curb and redirect the ship, and of course solve the original problem, but we don't know about the excess of electrons on our surface, a scientist on board make hypothesis some minutes before the impact and thinks that the problem is a lack of electrons! (and uses some command to increment them, worsening the crash)

First question:

How a moving (and electrically charged) observer at constant speed could explain metals coming to him?

Meanwhile on the (B) ship, technicians thinks their ship surface is not charged at all, and the force is because their metal structure itself, they thinks (A) ship is the charged one, and they don't know what to do because they are neutral, and action should be taken at the (A) ship to neutralize it because attraction would occurs regardless of the sign of electric charge.

Second issue:

As it has not sense to ask which ship is moving at speed v, because it's relative, does it have sense to ask about charge sign? Is there some way to tell which sign is the own charge? It's possible to know inside a system the sign of the outside visible charge?

Help those ships captains... before they crash!. =)

Answer 1

You are working under the impression that the magnetic field from a moving charge is just like the magnetic field from a bar-magnet, so that it pulls pieces o metal in. Then you are getting confused, because in the rest-frame of the moving charge, there is no magnetic field. So how can the motion of the metal be explained?

A moving charge's magentic field, does not go into and out of the charge like a bar-magnet's. It must go around the line of motion in circles, like the field from a current carrying wire, and this is required by symmetry. The magnitude of the field falls off as $1/r^2$ where r is the distance from the moving point.

But in addition, there is a $1/r^2$ electrostatic field, which has dominant effects. The electric and magnetic effects only become comparable as the spaceship gets close to the speed of light.

Whatever effect you ascribe to the magnetic field in the moving frame, you ascribe to the electric field when the ship is stationary. So the metal pulled into you by a combination of magnetic/electric field gradients is now pulled in by just an electric field gradient. The combined electric-magnetic field combination is called the F tensor, and the transformations required for these quantities to avoid any paradoxes of relative motion were worked out by Einstein in 1905, in the special relativity paper.

As for determining the sign of the charge, you can't do it just be looking at the motion of macroscopic objects, because you don't know their charge. But if you see some stray particles wandering by your ship, they will deflect outward or inward according to the charge of your ship, and the light particles are negatively charged electrons, the heavy ones are positively charged nuclei.