the mpi publication, finally!

[lectures/latex.git] / solid_state_physics / tutorial / 1_04.tex

diff --git a/solid_state_physics/tutorial/1_04.tex b/solid_state_physics/tutorial/1_04.tex
index 0fc68a6..2ec96f6 100644 (file)
--- a/solid_state_physics/tutorial/1_04.tex
+++ b/solid_state_physics/tutorial/1_04.tex
@@ -49,7 +49,7 @@ An electric field $E_x$ is applied to a wire extending in $x$-direction
 and a current density $j_x$ is flowing in that wire.
 There is a magnetic field $B$ pointing in the positive $z$-direction.
 Electrons are deflected in the negative $y$-direction
-due to the Lorentz force $F_L=-evB$
+due to the Lorentz force $F_L=-ev\times B$
 until they run against the sides of the wire.
 An electric field $E_y$ builds up opposing the Lorentz force
 and thus preventing further electron accumulation at the sides.
@@ -66,10 +66,12 @@ The two quantities of interest are:
 \end{itemize}
 In this tutorial the treatment of the Hall problem is based on a simple
 Drude model analysis.
-\\\\
+
 First of all the effect of individual electron collisions can be expressed
-by a frictional damping term into the equation of motion for the momentum 
+by a frictional damping term in the equation of motion for the momentum 
 per electron.
+By inserting the forces acting on the elecron into the equation of motion
+the expression for the Hall coefficient $R_H=-\frac{1}{ne}$ can be found.
 
 \begin{enumerate}
  \item Recall the Drude model. 
@@ -94,6 +96,17 @@ per electron.
        To find an expression for the Hall coefficient use the second  equation
        and the fact that there must not be transverse current $j_y$
        while determining the Hall field.
+ \item Calculate the Hall field for a rectangular wire
+       (width: $l=15\, cm$, thickness: $d=4\, mm$) made out of silver
+       if there is a current $I=200\, A$ flowing
+       and a magnetic field $B=1.5\, Vs/m^2$ applied
+       perpendicular to the current.
+       Silver has the relative atomic mass $A_r=107.87$ and
+       density $\rho=10.5\, g/cm^3$.
+       Assume that there is one valence electron per atom.
+       The atomic mass unit is $u=1.6605 \cdot 10^{-27} \, kg$
+       and $e=1.602 \cdot 10^{-19} \, As$.
+       {\bf Hint:} Start by calculating the Hall coefficient of silver first.
 \end{enumerate}
 
 \end{document}