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% 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}

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