ass3: Draft 8 as the deadline has already passed

.gitignore

@@ -47,3 +47,6 @@ superconductivity_assignment1_kvkempen.pdf
 
 # Assignment 2
 superconductivity_assignment2_kvkempen.pdf
+
+# Assignment 3
+superconductivity_assignment3_kvkempen.pdf

makefile

@@ -6,3 +6,6 @@ ass1:
 
 ass2:
 	latexmk -xelatex superconductivity_assignment2_kvkempen
+
+ass3:
+	latexmk -xelatex superconductivity_assignment3_kvkempen

superconductivity_assignment3_kvkempen.tex

@@ -0,0 +1,87 @@
+\documentclass[a4paper, 11pt]{article}
+\usepackage[utf8]{inputenc}
+
+\usepackage[
+	a4paper,
+	headheight = 20pt,
+	margin = 1in,
+	tmargin = \dimexpr 1in - 10pt \relax
+]{geometry}
+
+\usepackage{fancyhdr} % for headers and footers
+\usepackage{graphicx} % for including figures
+\usepackage{booktabs} % for professional tables
+\setlength{\headheight}{14pt}
+
+
+\fancypagestyle{plain}{
+	\fancyhf{}
+	\fancyhead[L]{\sffamily Radboud University Nijmegen}
+	\fancyhead[R]{\sffamily Superconductivity (NWI-NM117), Q3+Q4}
+	\fancyfoot[R]{\sffamily\bfseries\thepage}
+	\renewcommand{\headrulewidth}{0.5pt}
+	\renewcommand{\footrulewidth}{0.5pt}
+}
+\pagestyle{fancy}
+
+\usepackage{siunitx}
+\usepackage{hyperref}
+\usepackage{float}
+\usepackage{mathtools}
+\usepackage{amsmath}
+\usepackage{todonotes}
+\setuptodonotes{inline}
+\usepackage{mhchem}
+
+\newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}}
+
+\title{Superconductivity - Assignment 3}
+\author{
+	Kees van Kempen (s4853628)\\
+	\texttt{k.vankempen@student.science.ru.nl}
+}
+\AtBeginDocument{\maketitle}
+
+% Start from 8
+\setcounter{section}{7}
+
+\begin{document}
+
+\section{\ce{Nb3Sn} cylinder}
+Consider a cylinder of \ce{Nb3Sb}.
+From lecture 4, we have the following properties for \ce{Nb3Sn}:
+$T_c = \SI{18.2}{\kelvin}$,
+$\xi = \SI{3.6}{\nano\meter}$,
+$\lambda = \SI{124}{\nano\meter}$,
+$\kappa = \frac{\lambda}{\xi} = 34 > \frac{1}{\sqrt{2}}$,
+which means we are indeed dealing with a type-II superconductor.
+As $B_{c1} < B_E < B_{c2}$, the cylinder is in the vortex state.
+From the previous set of assignments, we know what the currents in the cylinder look like.
+
+The average field inside the cylinder is gives as
+\[
+	\langle \vec{B} \rangle = \frac{1}{V_{\text{cylinder}}} \int_{\text{cylinder}} \vec{B}(\vec{r}) d\vec{r} .
+\]
+
+To determine this $\vec{B}$ inside the material, we first need to know how many vortices there are.
+We assume that every vortex lets through only one flux quantum $\Phi_0$,
+and that the vortices will arange themselves as far as possible from eachother.
+If their distance then is large enough to assume there is no overlap between regions of finite $\vec{B}$ around them,
+we can calculate the average field by just summing over the quanta and lastly over the field that penetrates the material in the outside of the cylinder.
+For this latter calculation, we can use the field for a type-I superconductor.
+
+\section{Superconducting wire}
+
+\section{Fine type-II superconducting wire}
+
+\section{Critical currents}
+
+\section{A weak junction}
+
+
+\bibliographystyle{vancouver}
+\bibliography{references.bib}
+
+%\appendix
+
+\end{document}