Would throwing a charged ruler through space create a current?

Question

I have been thinking about a certain scenario for a while and have a few questions concerning it

Consider the scenario where I rub a ruler against a woolen cloth creating a negative charge of $1$ coulomb on the ruler, now if I were to throw the charged ruler horizontally in the air, since the ruler is moving and it is charged, would that qualify as a current?

Furthermore, if there truly is a current flowing since current flows from high potential to low potential would this mean that there is now a potential difference created in the space where the ruler is thrown, and if the current were to be flowing would, by Ampere's law, the current also produce a magnetic field?

And finally let us say that there is a magnetic field produced by the ruler, if I were to place a magnet somewhere along the rulers trajectory there would be a magnetic force exerted on it, now were I to throw the same magnet parallel to the ruler at the same velocity, since relative to the magnet the ruler is stationary thus there is no current flowing would there be no magnetic force acting between the two objects?

Answer 1

Would throwing a charged ruler through space create a current?

Yes, it would be a current.

would, by Ampere's law, the current also produce a magnetic field?

Yes.

And finally let us say that there is a magnetic field produced by the ruler, if I were to place a magnet somewhere along the rulers trajectory there would be a magnetic force exerted on it

Yes.

now were I to throw the same magnet parallel to the ruler at the same velocity, since relative to the magnet the ruler is stationary thus there is no current flowing would there be no magnetic force acting between the two objects?

That depends upon the frame of reference.

In the frame of reference of the ruler and magnet, which are not moving relative to one another, there is no magnetic field induced by the ruler, but only by the magnet. Hence there will be no force upon the ruler or magnet.

In a frame of reference where the ruler and magnet are both moving, relative to some observer, there is a magnetic field induced by the ruler. However, there is also an electric field created by the moving magnetic field. The net result will be no net apparent force.

As far as the ruler is concerned, the result can be calculated using the Lorentz force. The magnet must have an equal and opposite force on it. (Which will be zero in the last case). I am not aware of it's name, but there must be an equivalent to the Lorentz force for magnetic dipoles. Perhaps someone on this site knows the name and can give it to us.

Answer 2

Where do you envisage any possible current could flow, either through space or through the ruler. There are only two components here, space and the ruler, and although a local magnetic field could be created by the charged ruler, because it has a constant velocity there will be no potential difference between its ends.