Does Hyperbolic Motion Cause Particle Radiation?

[cragar]

Homework Statement

Does a particle in hyperbolic motion radiate?

The Attempt at a Solution

Griffiths say to use these 2 equations.
$w(t)= \sqrt{b^2+(ct)^2}$
$p= \frac{\mu_0q^2a^2 {\gamma}^6}{6\pi c}$
gamma is the Lorentz factor
w(t) is a function of time that describes position. now do I take the first derivative with respect to position to get v so I can plug that into the power equation and then take the derivative again to get a. I'm assuming that b is a constant. any help will be much appreciated.

 

[gabbagabbahey]

now do I take the first derivative with respect to position to get v so I can plug that into the power equation and then take the derivative again to get a. I am assuming that b is a constant.

Yes and yes. You should find that the power radiated is constant(!)

 

[TSny]

Does a particle in hyperbolic motion radiate?

Cragar, that's a fairly famous question that I don't think has been definitively answered. I'm certainly not qualified to answer it. I think Pauli once argued that there should be no radiation for hyperbolic motion. For an interesting discussion, see http://www.mathpages.com/home/kmath528/kmath528.htm