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\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}