- #1

genxium

- 141

- 2

##\frac{dP(t')}{d\Omega} = \frac{e^2\dot{u}}{16\pi^2\epsilon_0c^3}\frac{sin^2\theta}{[1-(u/c)cos\theta]^5}##

where ##t'## is retarded time, ##\theta## is the polar angle of measuring point in current spherical coordinate, ##u## is the value of velocity, ##\dot{u}## is the value of acceleration.

By differentiating wrt ##cos\theta## I can verify equation (1662) in the tutorial saying that

##\theta_{max} = arccos [\frac{1}{3(u/c)}(\sqrt{1+15u^2/c^2} - 1)]##

is the angle of maximum radiation.

However I don't get why taking ##u/c \rightarrow 1## results in ##\theta_{max} \rightarrow 1/(2\gamma)## where ##\gamma## should be ##\frac{1}{\sqrt{1-u^2/c^2}}##.

It seems quite straight forward for me to get just ##\theta_{max} \rightarrow arccos(1) \, = \, 0## as ##u/c \rightarrow 1##.

Where did I go wrong?

Any help is appreciated :)