From 580c6daf2748aeca527eacc86dcf7bcd599dd7e4 Mon Sep 17 00:00:00 2001
From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Mon, 10 Dec 2007 17:04:22 +0100
Subject: [PATCH] finished solution for tutorial 4 + added hall fig

---
 solid_state_physics/tutorial/1_04s.tex | 25 ++++++++++++++++-
 solid_state_physics/tutorial/hall.fig  | 37 ++++++++++++++++++++++++++
 2 files changed, 61 insertions(+), 1 deletion(-)
 create mode 100644 solid_state_physics/tutorial/hall.fig

diff --git a/solid_state_physics/tutorial/1_04s.tex b/solid_state_physics/tutorial/1_04s.tex
index b5d60e3..d99b994 100644
--- a/solid_state_physics/tutorial/1_04s.tex
+++ b/solid_state_physics/tutorial/1_04s.tex
@@ -60,7 +60,30 @@
        \stackrel{dt\rightarrow 0}{\Rightarrow} \quad
        \frac{dp(t)}{dt}=-\frac{p(t)}{\tau}+f(t)
        \]
- \item
+ \item \includegraphics[width=14cm]{hall.eps}
+ \item \[
+       \frac{dp}{dt}=-e\left(E+\frac{p}{m}\times B\right)-\frac{p}{\tau}
+       \]
+       steady state ($\frac{dp}{dt}=0$):
+       \begin{itemize}
+       \item $x$ component: $0=-eE_x-\frac{eB}{m}p_y-\frac{p_x}{\tau}$
+       \item $y$ component: $0=-eE_y-\frac{eB}{m}p_x-\frac{p_y}{\tau}$
+       \end{itemize}
+       setting $j_y$ to zero in the second equation ($\Rightarrow p_y=0$):
+       \[
+       E_y=-\left(\frac{B}{m}\right)p_x
+          \stackrel{j=-ne\frac{p}{m}}{=}-\left(\frac{B}{ne}\right)j_x
+       \]
+       \[
+       \Rightarrow R_H=-\frac{1}{ne}
+       \]
+ \item \begin{itemize}
+        \item electron density: $n=\frac{V\rho}{A_ru}/V=\frac{\rho}{A_ru}$
+        \item $R_H=-\frac{1}{ne}=-\frac{A_ru}{e\rho}$
+	\item $j_x=\frac{I}{ld}$
+	\item $E_{Hall}=E_y=R_HBj_x=\ldots=5.3 \cdot 10^{-5} \, \frac{V}{m}$
+	\item $U_{Hall}=E_y l=\ldots=-7.95 \, \mu V$
+       \end{itemize}
 \end{enumerate}
 
 \end{document}
diff --git a/solid_state_physics/tutorial/hall.fig b/solid_state_physics/tutorial/hall.fig
new file mode 100644
index 0000000..c12b8a0
--- /dev/null
+++ b/solid_state_physics/tutorial/hall.fig
@@ -0,0 +1,37 @@
+#FIG 3.2  Produced by xfig version 3.2.5
+Landscape
+Center
+Metric
+A4      
+100.00
+Single
+-2
+1200 2
+2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 2565 3780 7560 3780 7560 4230 2565 4230 2565 3780
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+	 2565 3780 4275 2070
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+	 4275 2070 9225 2070
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+	 7560 3780 9270 2070
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 3.00 60.00 120.00
+	 5805 3015 5805 1575
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 3.00 60.00 120.00
+	 8505 3105 9405 3105
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 3.00 60.00 120.00
+	 2385 2925 3285 2925
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 4
+	 7560 4230 9270 2520 9270 2070 9090 2070
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 60.00 120.00
+	 7155 2565 6480 3240
+4 0 0 50 -1 0 12 0.0000 6 180 540 2475 2790 $E_x$\001
+4 0 0 50 -1 0 12 0.0000 4 105 4605 4320 2250 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +\001
+4 0 0 50 -1 0 12 0.0000 4 60 3315 2835 3735 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -\001
+4 0 0 50 -1 0 12 0.0000 6 165 345 5850 2475 $B$\001
+4 0 0 50 -1 0 12 0.0000 6 195 540 6975 2970 $E_y$\001
+4 0 0 50 -1 0 12 0.0000 6 195 480 8955 2970 $j_x$\001
-- 
2.20.1