Does a rotating ring of charge radiate power or not? The Larmor Formula suggests that the power radiated by an accelerating charge is non zero. But we know that a uniformly charged non-conducting ring rotating about its central axis does not radiate. Why is this so? 
This is somehow very strange to me. For example, suppose I charge a very small portion of the non conducting ring with charge q. Now when I rotate this ring with a constant angular velocity, there should be radiation. Now, all I have to do is spray some charge uniformly on the rotating ring, and the radiation just ceases! Isn't this strange? We can negate radiation simply by spraying charge carefully? 
Please explain why there is no radiation in this case.
 A: To radiate, you must have a fluctuation with time
If you take a small portion of the ring, charge it, and then make it rotate, the distribution of charges does change with time.
If the ring is evenly charged, with no additional currents, and you make the ring rotate, then in this (ideal) situation the distribution of charges between two times is always the same. There would be no way to differentiate the situation at $t_1$ and $t_2$, so no radiation. I assume that if you compute the EM fields radiated by each charge, and sum them over the ring, they cancel out.
A: Photons are their own anti-particle and can cancel out. Or put another way, light is a wave and waves can destructively interfere. 
With the rotating ring of charge, there are many radiating fields, but the symmetry of the problem lets them cancel destructively so there is no net wave and no power lost to radiation. Radiation here is just an EM wave carrying power.
Think of a somewhat similar situation from electrostatics: If you add electrical charge to a perfect conductor, the charges arrange themselves on the surface and the electric field is 0 within the conductor. There are many charges with many fields, but they all cancel out. This is easiest to calculate for a sphere, in case you want to try it.
A: I address this question in my answer Why don't loop currents produce light?.  As you divide the single charged particle into more and more pieces while keeping the total charge and average current fixed, the charge distribution varies less and less over time and the radiated power smoothly decreases to zero.
