# Would throwing a charged ruler through space create a current?

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?

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.

• The force on a magnetic dipole doesn't have a name other than "the force on a magnetic dipole" as far as I know; but for point dipoles $\vec{m}$ in vacuum it's $\vec{F} = (\vec{m} \cdot \vec{\nabla}) \vec{B}$. Commented May 13, 2021 at 14:21

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.

• Then how would you explain how the solar wind interacts with Earth's magnetic field? Every one of those protons is effectively a charged ruler. Commented May 13, 2021 at 23:15
• The effect of a solar wind on earth's magnetosphere is a different circumstance to a charged ruler in constant velocity in free-space. If that ruler was to pass through a magnetic field in a quadrature direction to the lines of force it could then induce local currents in the ruler dependent on where the charged electrons were situated on its surface. A charged ruler of this nature actually has very few static free electrons although when a ruler is rubbed in this way if seems to exhibit quite a high characteristic field to our touch. A solar wind in our magnetosphere creates a photon plasma. Commented May 15, 2021 at 23:16