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%TCIDATA{Created=Tue Nov 26 09:32:41 1996}
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%TCIDATA{Language=American English}

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\markright{{\sf Classical Radiated Power    }}
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\section{14.2\quad Classical Radiated Power.}

\subsection{14.2.1}

\quad \thinspace \textbf{a. }The radiated fields are due to the last term in
(14.1.9). In the non-relativistic limit, $\beta \ll 1,$ $R=r=s$ and the
radiated fields are 
\begin{eqnarray*}
\mathbf{E} &=&\frac ec\frac{\mathbf{\dot{\beta}}_{\perp }}R \\
&& \\
\mathbf{B} &=&\frac{\mathbf{R}}R\times \mathbf{E\,.}
\end{eqnarray*}

\smallskip\ 

\textbf{b}. The Poynting vector is in the direction of $\mathbf{R}$ and has
magnitude $(c/4\pi )\mathbf{E}^2.$ The instantaneous power radiated is 
\begin{equation}
\frac{dP}{d\Omega }=\frac c{4\pi }R^2\mathbf{E}^2=\frac{e^2}{4\pi c^3}%
\mathbf{\dot{v}}^2\sin ^2\Theta \,.  \label{1}
\end{equation}

\smallskip\ 

\textbf{c. }The total radiated power is 
\[
P=\frac 23\frac{e^2}{c^3}\mathbf{\dot{v}}^2. 
\]
This is \textsl{Larmor's formula.}

\smallskip\ 

\textbf{d. }The generalization of these results to arbitrary values of $%
\beta $ is taken up in the next sections.

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