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+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics I}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ WS 2007/08\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 2 - proposed solutions}
+\end{center}
+
+\section{Drude theory of metallic conduction}
+\begin{enumerate}
+ \item $U=IR \Rightarrow EL=jA\rho\frac{L}{A}
+             \Rightarrow E=j\rho$
+ \item distance: $v\,dt$\\
+       number of electrons crossing $A$: $n(v\,dt)A$\\
+       $\Rightarrow$ $j=\frac{I}{A}=\frac{dQ/dt}{A}=\frac{-e\,n(v\,dt)A/dt}{A}
+                       =-nev$
+ \item \begin{itemize}
+        \item In the absence of an electric field, electrons are as likely
+	      to be moving in any one direction as in any other.
+	      The velocity averages to zero.
+	      As expected, according to the above equation, there is no
+	      net electric current density.
+        \item Since electrons emerge in a random direction
+	      there will be no contribution from the thermal velocity
+	      to the average electronic velocity.
+        \item $v_{average}=at=\frac{F}{m}\tau=-\frac{eE}{m}\tau$
+       \end{itemize}
+ \item \begin{itemize}
+	\item $j=\left(\frac{ne^2\tau}{m}\right)E$\\
+	\item $j=\sigma E \Rightarrow \sigma=\frac{ne^2\tau}{m}$
+       \end{itemize}
+ \item Energy transfer: $\frac{m}{2}v_{drift}^2$,
+                        $\qquad v_{drift}$:
+			end drift velocity of the accelerated electron\\
+       $v_{drift} \ne v_{average}$
+
+       
+\end{enumerate}
+
+\end{document}