Do Accelerated Charges Always Radiate?

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In summary, the conversation discusses the radiation of charges when accelerated, specifically focusing on the cases of opposite charges and dipoles and quadrupoles. It is determined that opposite charges, when accelerated, produce oppositely directed magnetic fields, resulting in no net field. The conversation also delves into the concept of nonradiative motions and the conditions for radiation to occur.
  • #1
shoestring
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Assume two charges, an electron and a proton, accelerate together. For example, let them start at (x,y)=(0,h) and (0,-h) and move in the +x direction along parallel trajectories (x(t),h) and (x(t),-h) while accelerating.

If they are far apart I assume they will each radiate on its own, but what happens if they are close, or even combine to form a hydrogen atom? When will they stop radiating?

Any neutral piece of materia made up of electrons, neutrons and protons consists of charges, so why doesn't a neutral piece of materia radiate under acceleration?

In short: When do accelerated charges radiate and when don't they?
 
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  • #2
shoestring said:
Assume two charges, an electron and a proton, accelerate together. For example, let them start at (x,y)=(0,h) and (0,-h) and move in the +x direction along parallel trajectories (x(t),h) and (x(t),-h) while accelerating.

If they are far apart I assume they will each radiate on its own, but what happens if they are close, or even combine to form a hydrogen atom? When will they stop radiating?

Any neutral piece of materia made up of electrons, neutrons and protons consists of charges, so why doesn't a neutral piece of materia radiate under acceleration?

In short: When do accelerated charges radiate and when don't they?

This is not my strongest area, but I think it is that opposite charges, when accelerated, will produce oppositely directed magnetic fields, so there is no net field. I am eager, though, to see comments from someone with a stronger background.
 
  • #3
Thanks, that makes sense. What happens to the fields is perhaps more important than the acceleration of the charges itself.

A slightly different question: If a dipole is accelerated, will it radiate?
 
  • #4
Yes, they will radiate. Although this is not obvious!

Let d be the position vector of the midpoint of the two particles, and h the vector from there to particle 1. The particles will be located at r1 = d + h and r2 = d - h. The dipole moment will be p = ∑ qi ri = e(d + h) - e(d - h) = 2eh. So what, you say? The point is that p is constant. You can't possibly get dipole radiation from the charges, since their dipole moment is constant.

Ok, now look at the quadrupole moment. Q = ∑ qi riri = e(d + h)(d + h) - e(d - h)(d - h) = 2e(dh + hd). So what, you say? The point is that Q is *not* constant. Since you can choose d(t) to be anything you like, Q can also be made to vary in time in any way you like. So in general you can get quadrupole radiation. But there's a condition that must be imposed on d(t).

E & M books are so quick to Fourier transform everything, it's hard to find a radiation formula that still has t dependence in it. In Jackson, for example, the radiated power of an oscillating dipole is given as P = ck4/3 |p|2. If he hadn't Fourier transformed it, this would have been P = c/3 |p(2)|2, where (2) means the second time derivative. A few pages later, the power from an oscillating quadrupole is given as P = ck6/360 |Q|2. Meaning P = c/360 |Q(3)|2. In general, the radiation formula for the mth multipole moment will have m+1 time derivatives on it.

The point here is that not just any time dependent p or Q will radiate. You need a p such that p(2) is nonzero. Likewise you need a Q such that Q(3) is nonzero. Solutions for which p ~ t or Q ~ t2 do *not* radiate. These are called nonradiative motions.

In the present problem, if you use a constant acceleration d(t) = at2/2, then Q(t) ~ d(t) ~ t2 is a nonradiative motion. You'll get quadrupole radiation if and only if the acceleration is not constant.
 
  • #5
Great post Bill.
 

1. Will all objects radiate?

No, not all objects will radiate. The ability to radiate energy is dependent on an object's temperature and material composition.

2. How do objects radiate energy?

Objects radiate energy through electromagnetic radiation, which is the emission of energy in the form of waves or particles.

3. What factors affect the amount of radiation an object emits?

The amount of radiation an object emits is affected by its temperature, surface area, and material composition.

4. Can radiation be harmful?

Yes, some forms of radiation, such as ionizing radiation, can be harmful to living organisms. However, not all forms of radiation are harmful.

5. How can we measure the amount of radiation emitted by an object?

We can measure the amount of radiation emitted by an object using a device called a radiometer, which detects and measures electromagnetic radiation.

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