I was interested in the conditions where electron acceleration lead to radiation and where they don't. I've been wanting to ask about this for awhile, but I didn't want to side track things.
The experiment with charge placed on a spinning disk was interesting. If I understand things, as long as the charge is evenly distributed around the disk when the disk is spun there is no radiation.
Correct, assuming the rate of spin is also unchanging.
However, if the charge is placed unevenly around the disk , when the disk is spun there is radiation.
That depends. If the charge is placed evenly around the rim of the disk, then the charge is not the same over the entire disk, yet there is still no radiation.
Could somebody talk a little bit about what is going on here qualitatively?
If the current density vector field
J doesn't change with time, then there is no radiation because the electric and magnetic fields induced by the charge and current will be independent of time, with ∂
E/∂t = ∂
B/∂t = 0.
When the charge is distributed evenly over the entire surface of a spinning disk, or evenly around its rim, then at every point of space the current density
J will be independent of the time t.
If the charge is placed on a spot that isn't centered on the center of the disk, then the current density
J will change at points on that spot's trajectory. When a fixed point of space intersects the charged spot, the current density will be nonzero, but the current density will go to zero at that point when the charged spot moves away from the point. In that case, the current density
J will be a cyclic (periodic) function of time at every point, ∂
E/∂t and ∂
B/∂t will not be identically zero at all times, and radiation will ensue.
What is going on at the individual charge level? How does an individual electron decide whether it is going to radiate or not? Is it sort of a net effect deal where all the individual electrons are radiating no matter what but in the evenly dispersed charge case the radiation from individual electrons cancels out any net radiation? Or does somehow the distribution of charge prevent the electrons from radiating at all?
Because charge is quantized, you could say that a perfectly uniform distribution of charge is not possible. On the other hand, quantum mechanics tells us we cannot simultaneously measure both the position and momentum (hence current) of an electron with perfect precision. If we can't measure an electron's position and current with enough precision to detect changes in the current density at some position, then we won't detect any radiation (because detection of radiation would be one way to detect changes in the current density at a position).
In terms of a spinning disk, a constant current density is maintained so long as every charge that moves away from a point is immediately replaced by another charge moving into the point. That isn't quite true, but with 6×10
18 electrons per second in an ampere of current, and a charge confined to the surface of the disk so there's only a small area perpendicular to the current through which the current flows, it's a darned good approximation.
It's important to note here that
any direct current would have essentially the same issue. No one would claim that an unvarying direct current running through a straight wire will radiate just because the charges are quantized. No one should claim that a uniformly charged and uniformly spinning disk will radiate either.
Could somebody talk about what's going on energy wise here? When the charge is unevenly distributed the system is losing energy. Where is that energy coming from? Is the spinning disk slowed by the radiation or is the disk losing mass?
I'll leave that one for the physicists to answer.