Question about orbiting charges

[Inquisiter]

Imagine a charge (I'm talking about CLASSICAL charges, NOT electrons in an atom) which is orbiting amother much more massive charge. The charge will radiate, call the power it radiates p. Now imagine a charge spinning on it's axis (but not orbiting, just spinning), it will also radiate(we can divide the charge into small chunks, these chunks are accelerating, so they radiate), call the power q. Now if the charge is BOTH orbiting another charge and spinning on it's axis (with the same angular velocity), will the radiated power be p+q? If not, when will it be at least approximately p+q? Will the radiated power depend of the tilt of the axis of the charge?

Follow up question: Can we talk about the instantaneous power that a charge is radiating, or can we only talk about average power? Why or why not?

 

[shyboy]

The spinning charge will not radiate, because the electric and magnetic field will be constant and time independent. Or yor may say that the radiation from different "chunks" will cancel each other.

Of course we can speak about the instant power.

 

[shyboy]

Now, if we consider the charge both orbiting and spinning, then the radiated power will be different, because you will have an oscillating quadrupole magnetic moment. If their frequency are not harmonics, then we can average the radiated power separetely.

 

[Inquisiter]

The spinning charge will not radiate, because the electric and magnetic field will be constant and time independent. Or yor may say that the radiation from different "chunks" will cancel each other.

Hm, I was sort of suspecting that... It's just that I read that electrons in a superconductive ring are accelerating and must radiate according to classical physics, and the reason they don't radiate is quantum mechanical. I guess that classically for the spinning sphere or ring to not radiate the distribution of charge must be continous. Otherwise, the radiation from different chunks (electrons in this case) won't completely cancel each other. So classically, the electrons in a superconductive ring WOULD radiate (although the radiation would be very weak)? So, if you have two positive charges on the different ends of a spinning rod, the radiation will be very weak, since the radiation from one charge pretty much cancels the radiation from another charge. But what if the rod is spinning so quickly that the wavelength is much shorter than the length of the rod? Will the radiation be significant then? OH, or is that not even possible since the charges can't be moving faster than light?!

 

[shyboy]

The electrons in a superconducting ring will not radiate for classical reasons, because all the multipoles would be constant. Classical QM itself cannot forbid the radiation from the superconducting ring, because in classical QM radiation occurs during the transition between the different states. The superconducting ring can have many states just like atom has. But to calculate the probability of the transition we need to use the classical electrodynamics.