diff --git a/superconductivity_assignment3_kvkempen.tex b/superconductivity_assignment3_kvkempen.tex index 25f1a41..f2263e0 100755 --- a/superconductivity_assignment3_kvkempen.tex +++ b/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}