# Magnetic field of a charged rod

dubvmet
moving charged particles created a magnetic field perpendicular to their motion I believe. Anyways If you where to give a metal rod a positive or negative charge and spun it really fast would you created a noticeable magnetic field as a result of the moving rod as a whole?

Its just a thought experiment I was thinking of and wanted to know the answer.

Homework Helper
Gold Member
Hello dubvmet,

Welcome to Physics Forums!

moving charged particles created a magnetic field perpendicular to their motion I believe. Anyways If you where to give a metal rod a positive or negative charge and spun it really fast would you created a noticeable magnetic field as a result of the moving rod as a whole?

Its just a thought experiment I was thinking of and wanted to know the answer.

"Noticeable" is a somewhat subjective term, but measurable, yes. As a matter of fact if you were to spin such a rod around you would create an electromagnetic field that would propagate through space (it might be very small, yet measurable with instrumentation, if the instrumentation was close to it). But it wouldn't be a constant magnetic field, rather it would be oscillating. In other words, you couldn't use it like you would a bar magnet.

bjacoby
moving charged particles created a magnetic field perpendicular to their motion I believe. Anyways If you where to give a metal rod a positive or negative charge and spun it really fast would you created a noticeable magnetic field as a result of the moving rod as a whole?

Its just a thought experiment I was thinking of and wanted to know the answer.

Since it's a thought experiment, lets think about it!

This is a very interesting question because it is an electrostatic analogy to the old magnetic one asked by Faraday: Does a magnetic field rotate with a magnet? In this case we know that if we charge a metal rod the charge redistributes itself to the outside of the object. We also know from symmetry that the electric field about the rod has axial symmetry. So that if you rotate the rod, the mathematical description of the static electric field stays the same. So that raises a question: Does the electric field rotate about a rotating charged rod? Interesting!

But then for a rotating METAL rod one must ask one more question: Does the charge on the outside of the rod rotate with the rod if you spin it. If it does, then that clearly defines a current and current clearly creates a magnetic field. Hence it would appear that if one had an INSULATOR rod that a magnetic field would ensue. But a metal one is a different thing in that the charge is free to a degree to travel about the outside of the rod. Thus there exists a thing known as "relaxation time" which is a measure of how fast charge moves on a metal rod. So now it seems part of the answer involves how FAST we are spinning the rod. And the final consideration would be exactly WHAT would produce a dragging force on the charges keeping them from spinning with the rod. The answer would seem to be that their fields (even going to infinity) provide an attractive force to something. The idea is obvious if you consider a coaxial capacitor with the center terminal spinning.

So as I see it, this is an interesting question but there seems to be no easy answer except under certain conditions.

And let me note that when you have relative motion between frames there are created apparent magnetic and electric fields just from that motion! Even "neutral currents" (equal + and - charges moving in opposite directions giving no net total charge can) create electric fields when in motion. Nothing is ever quite as simple as it seems!