From a98ac11704297fd5f8701895f0a9b3cfa2376d47 Mon Sep 17 00:00:00 2001 From: hackbard Date: Thu, 6 Dec 2007 14:33:52 +0100 Subject: [PATCH] finished tutorial 4 --- solid_state_physics/tutorial/1_04.tex | 19 ++++++++++++++++--- 1 file changed, 16 insertions(+), 3 deletions(-) diff --git a/solid_state_physics/tutorial/1_04.tex b/solid_state_physics/tutorial/1_04.tex index 0fc68a6..2ec96f6 100644 --- 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} -- 2.20.1