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\title{Superconductivity - Assignment 3}
\author{
	Kees van Kempen (s4853628)\\
	\texttt{k.vankempen@student.science.ru.nl}
}
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\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}


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%\appendix

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