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11: 9a done i think

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Kees van Kempen
2022-03-17 14:58:13 +01:00
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superconductivity_assignment3_kvkempen.tex
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@ -102,6 +102,16 @@ For the gradient we thus find
The size of the supercurrent density has the same relation, $J_S \propto 1/r$. The size of the supercurrent density has the same relation, $J_S \propto 1/r$.
\section{Superconducting wire} \section{Superconducting wire}
The voltage $U = \SI{1.5e-5}{\volt}$ across the wire of length $\ell = \SI{.08}{\meter}$ induces a current $J_t$. % through the resistive wire with unknown resistivity $\rho$ according to Ohm's law.
Due to the presence of the magnetic field $B = \SI{5}{\tesla}$, if the vortices move with velocity $v_L$, a Lorentz force $f_L$ per vortex acts on the vortices.
This results in a power input $P_L = f_Lv_L = J_tBv_L$ per vortex.
%$\epsilon = Bv_L$
This power should come from the current induced by the voltage, thus $P_L = \epsilon J_t = \frac{U}{\ell}J_t$.
Equating these expressions and rewriting yields
\[
v_L = \frac{U}{B\ell} = \SI{3.75e5}{\meter\per\second}.
% https://www.wolframalpha.com/input?i=1.5*10%5E-5+%2F+%285*+.08%29
\]
\section{Fine type-II superconducting wire} \section{Fine type-II superconducting wire}