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{\bf SOLUTIONS FINAL ADVANCED DYNAMICS}\\ 
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\centerline{\bf PROBLEM 3}\bigskip

\noindent The electromagnetic field tensor is given by
Find (the Einstein summation convention is assumed for identical
indices):
\begin{enumerate}
\item $F^{\alpha}_{\ \ \alpha} = 0$. 
\item 
$$ (F_{\alpha\beta}) = \left( \matrix{ 
			      \ 0& +E^x& +E^y& +E^z \cr
			     -E^x&\ 0  & -B^z&\ B^y \cr
			     -E^y&\ B^z&\ 0  & -B^x \cr
			     -E^z& -B^y&\ B^x&\ 0 \cr}\right) \ . $$
\item $F_{\alpha\beta} F^{\alpha\beta}=2\,\left(\vec{B}^{\,2}-
\vec{E}^{\,2}\right)$.
\end{enumerate}
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