E-Field from Rotating Charged Rod: Cerenkov?

[cragar]

Lets say I have an infinite uniformly charged rod, and this charged rod is rotating like a barber pole. Let's say I am standing outside the rod, will I be able to tell if the source is rotating or will the E field be constant. Let's say the charged rod is wrapped with a dielectric
if the rod is rotating fast enough could there be Cerenkov radiation

 

[Simon Bridge]

Lets say I have an infinite uniformly charged rod, and this charged rod is rotating like a barber pole. Let's say I am standing outside the rod, will I be able to tell if the source is rotating or will the E field be constant. Let's say the charged rod is wrapped with a dielectric
if the rod is rotating fast enough could there be Cerenkov radiation

I'd expect all kinds of odd effects because you are describing a non-physical situation ... i.e. an infinite-length rotating line of charge would have some parts superluminal.

Loosely: for something like, say, the classical very-long uniformly charged rod rotating in vaccuum, I'd expect a varying E-field for most places you could stand, you'd be able to tell it was rotating (in your reference frame) because you'd be able to look at it and see, but I would not expect cherenkov radiation unless the whole setup was immersed in a dielectric medium.

I would not expect E to be constant even in the static (non-rotating) case - I'd expect the direction to be radial and the magnitude to decrease with radial distance. Hence the magnitude and direction will depend on where you measure it.

Where were you going with this?

 

[cragar]

I guess what I meant by constant E field is that at a point in space it is not varying with time. The rod does not need to infinite it can be finite. How would you be able to tell
that the cylinder was rotating without looking at it. What experiment would you be able
to do locally to tell that. Part of the reason I wanted it to be infinite is so there is no B field outside the rod. Maybe we should just have two charged concentric charged spheres and then have the inside sphere turning. What do mean when you say it needs to be immersed in a dielectric medium, why can't it just be surrounded by one.

 

[Simon Bridge]

Oh you mean rotating about it's axis?
Somehow I thought you meant rotating end-over-end.

Why not do the math?

 

[cragar]

use gauss's law or do a field transformation on the E field.

 

[BruceW]

I guess what I meant by constant E field is that at a point in space it is not varying with time. The rod does not need to infinite it can be finite. How would you be able to tell that the cylinder was rotating without looking at it. What experiment would you be able to do locally to tell that. Part of the reason I wanted it to be infinite is so there is no B field outside the rod.

To be sure, the E field will be constant with time if the rod is not spinning. And if the rod is spinning, that means there are charges being accelerated, so this (generally) causes radiation to be given off. So I would think you can use any old measuring instrument like an antenna, to pick up the radiation given off.

You wanted it to be infinite so that there is no B field outside the rod? Why does this imply zero B field? If you think about some general point, the moving currents on one side of the centre of the pole will be closer than on the other side, so the B field won't get canceled out.

I know how to calculate the (constant with time) parts of the E and B field (i.e. ignoring the fact that moving charges would cause radiation). But I am not familiar with calculating radiation given off...

 

[cragar]

The reason the B field is zero outside is because its an infinite solenoid and the current enclosed is zero in my amperian loop.
Ok yes sometimes accelerating charges radiate but is this true for a solenoid.
And is this true for an infinite uniformly charged rod.

 

[andrien]

sometimes accelerating charges radiate but is this true for a solenoid.
And is this true for an infinite uniformly charged rod.

why not.Also amperes law does not apply to electrodynamics.

 

[cragar]

ok this still doesn't address my original question about
Cerenkov radiation
plus I still don't think current loops radiate maybe look at this forum.
well they radiate if we consider points charges instead of a continuous charge distribution, but any way.
https://www.physicsforums.com/showthread.php?t=561208

 

[BruceW]

The reason the B field is zero outside is because its an infinite solenoid and the current enclosed is zero in my amperian loop.
Ok yes sometimes accelerating charges radiate but is this true for a solenoid.
And is this true for an infinite uniformly charged rod.

ah, duh! I forgot it is like a solenoid, because I normally think of a solenoid as a coil of wire. It is an interesting problem. In practice, the pole would need to be spinning pretty fast to be able to create a significant magnetic field. Also, there is the problem of what happens in the centre of the pole. Maybe the example of a pole which is hollow in the middle is a bit simpler/easier to work with.

Right, so if we're going to assume that there is zero magnetic field outside, then there won't be any energy emitted in the form of electromagnetic waves. Because there must be a non-zero magnetic field to allow energy to be propagated (simple use of Poynting vector). So if you want to find something which is going to emit EM energy, then its going to have to be not strictly a solenoid in this sense.

edit: out of curiosity, is this machine going to be used for some science fiction writing? or is it just general curiosity?

 

[cragar]

Ok my question isn't about the source radiating. Its about if the source causes Cerenkov radiation in the dielectric.
actually the point you make about the poynting vector might solve this.

 

[BruceW]

I'm still not sure what you mean by Cerenkov radiation. Isn't that usually generated when a charged particle is moving through a medium at a speed faster than the phase speed of light?

So in this situation, you've got a pole which is made of some uniformly charged medium... I don't see how there are charged particles moving through some medium with relative velocity...

 

[andrien]

the acceleration field vary as 1/r,it is necessary otherwise there will not be radiation detected at long distances.1/r² variation vanishes rather rapidly to give any contribution.The electric field which contains 1/r contribution contains acceleration of particles.For a charge particle moving through dielectric can radiate under condition of it's velocity surpassing the velocity of light in that medium evaluated by some refractive index formalism.That's all.if there is a solenoid in which current is time varying then there is a theoretical framework for calculating radiation from it.it is called multipole radiation.