11: 9a done i think

superconductivity_assignment3_kvkempen.tex

@@ -102,6 +102,16 @@ For the gradient we thus find
 The size of the supercurrent density has the same relation, $J_S \propto 1/r$.
 
 \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}