Do Current Loops Really Radiate Despite Accelerating Charges?

[cragar]

I think I was told that current loops don't radiate even though we have accelerating charges.
But why doesn't it radiate? Could we say something like the B field is symmetric and the electrons on the other side of the wire feel the presence from the other electrons.
If I had a line current in the shape of a U , would that radiate.

 

[chrisbaird]

I think I was told that current loops don't radiate even though we have accelerating charges.

All current loops radiate. At household voltages and frequencies, the radiation is so weak that it is typically negligible. At higher voltages/frequencies, such as in a particle accelerator, the radiation due to the charges looping can be quite dangerous (and useful).

But why doesn't it radiate? Could we say something like the B field is symmetric and the electrons on the other side of the wire feel the presence from the other electrons.

No, this is wrong. Radiation spreads out in all directions. You can't count on it all going to the other side of the loops and being absorbed.

If I had a line current in the shape of a U , would that radiate.

Yes. Consider turning on a kitchen blender, which is nothing more than an electric motor attached to a blade. When you turn it on, it creates radiation strong enough that an old CRT television with rabbit ears will pick up the radiation and its picture will go fuzzy. An electric motor is just a collection of magnets and loops of currents. (Yes, I realize that the current in an electric motor may be alternating, and the shaft is spinning, so the picture is more complex, but it's just an illustration).

 

[cragar]

so a dc constant current loop will radiate. And then a solenoid must radiate as well.

 

[chrisbaird]

Yes, but very weakly. Anytime a charge accelerates (which includes circular motion), it radiates. It's called Synchrotron radiation.

 

[Bill_K]

Disagree totally. A single charge moving in a circle will radiate. N equally spaced charges moving in a circle will radiate. This is because the electric and magnetic fields that they produce are time varying.

But as N → ∞, the current becomes a steady current, the time-varying fields go to zero, and the radiation goes to zero. A steady current does not radiate.

 

[technician]

Bill K is the closest to a sensible answer here.
Electrons flow ALONG a wire because there is an electric field between the ends of the wire.
The electrons follow the electric field lines (OK they are - charged so they are in the opposite direction to the lines... but they do follow the lines).
Making the wire a circle or an S shape or any other shape does not change the Electric field lines.
There is no force making electrons follow the circular path of a wire twisted into a circle.
They are not accelerating because the wire forms a circle !
FREE electrons (charged particles) must experience a force if they are to travel in a circular or curved path (usually provided by a magnet). These particles are accelerating because of their curved path and will radiate electromagnetic radiation. This radiation is known as Cyclotron or synchrotron radiation.
I am sure this is not rigorous but I hope it helps any further discussion.

 

[cragar]

@ technician, when you say they are not accelerating because the wire forms a circle. what about centripetal acceleration?

 

[technician]

The electrons are following electric field lines... there is no sideways force on them making them travel in a circular path... they are confined to the wire and follow the direction of the wire.
If the wire was placed in a magnetic field at right angles to the current flow then there would be a sideways force and the wire would be deflected but that is another point of discussion.

 

[Drakkith]

@ technician, when you say they are not accelerating because the wire forms a circle. what about centripetal acceleration?

I would guess that there is no centripetal acceleration. Each individual electron only moves a very very small distance, and only a fraction of the total electrons are moving.

 

[cragar]

what if I had a charged ring that I spun mechanically?

 

[Studiot]

Spinning the loop or not, Drakkith is right.

There is a huge difference between the speeds of electrons in wires and atoms, or say an electron beam operating at 100MHz.

Here are some official figures from the US government.

http://www.Newton.dep.anl.gov/askasci/phy99/phy99092.htm

Further when you divide by the radius (10^-11)) in an atom as against say 1 in a curved wire (to get the acceleration) you can calculate for yourself the difference in expected radiation.

go well

 

[Loro]

There is no force making electrons follow the circular path of a wire twisted into a circle.

Hmmm but there is a force - it comes from the fact that surface charge builds up in a wire - especially in the most curved parts - and this charge makes the E-field point always along the wire.

So when an electron passes a U-shaped part - it is repelled by electrons built up on the outer surface of U - which always build up is such a way, that they provide the required centripetal force to pass it.

So I'd rather someone smarter confirmed or corrected me on this part - but if it's all about the Coulomb force - I think it all boils down to the question why an electron rotating around a nucleus doesn't emit radiation. And the answer can be provided only by quantum mechanics - it always stays on the same quantum level.

And I guess a charge passing a U-shaped part of a wire always stays on the same quantum level of the whole configuration of the charges (the nuclei of the wire, the surface charges) - the same level in the wire's conduction band.

 

[cragar]

Spinning the loop or not, Drakkith is right.

There is a huge difference between the speeds of electrons in wires and atoms, or say an electron beam operating at 100MHz.

Here are some official figures from the US government.

http://www.Newton.dep.anl.gov/askasci/phy99/phy99092.htm

Further when you divide by the radius (10^-11)) in an atom as against say 1 in a curved wire (to get the acceleration) you can calculate for yourself the difference in expected radiation.

go well

I am not saying anyone is wrong, I am trying to understand.
What if I had a bunch of tiny little metal spheres that I charged up and then tied a rope to them and attached them to a central hub and then spun them around like a merry go round. I would think that these charged spheres would feel an acceleration. Even if the radiation is small, I just want to know if it will radiate. What if i had a non-uniform charge density. And the metal spheres are close by not touching,so the charge doesn't evenly distribute.

 

[Studiot]

You are presumably referring to the larmour equation for the radiated power (P) of an accelerating charge (q)

P = \frac{{{\mu _0}{q^2}{a^2}}}{{6\pi c}}Put some numbers into this equation and ask yourself if the radiation from a curved wire would be large enough to be detectable.

 

[cragar]

I could use a high energy ion beam inside a tokamak and that would be detectable if it radiated.

 

[Drakkith]

I could use a high energy ion beam inside a tokamak and that would be detectable if it radiated.

Or a CRT Electron Gun and a magnet.

 

[chrisbaird]

...But as N → ∞, the current becomes a steady current, the time-varying fields go to zero, and the radiation goes to zero. A steady current does not radiate.

That was my point. In real life N can never approach infinity, so all loops radiate. The steady-current approximation of magnetostatics is just that: an approximation (a very good one for low currents). I did not say the radiation would be detectable, just that the there would be radiation.

technician, if there were no force keeping electrons in a looped piece of wire, they would fly off in straight lines under simple inertia. Conduction electrons in metals are not truly free, but are bound to the solid in a delocalized way. It takes energy to break this bond and take an electron out of the metal (the work function). The binding force of the solid is what keeps the current in the wire even when you bend it in a loop, not any direct force you are providing with your hands by bending the wire.