the mpi publication, finally!

[lectures/latex.git] / solid_state_physics / tutorial / 2_02.tex

diff --git a/solid_state_physics/tutorial/2_02.tex b/solid_state_physics/tutorial/2_02.tex
index 5f280f0..b9b5c5a 100644 (file)
--- a/solid_state_physics/tutorial/2_02.tex
+++ b/solid_state_physics/tutorial/2_02.tex
@@ -56,9 +56,10 @@ and $\lambda$ is the London penetration depth.
        of the wire. Assume, that the penetration depth $\lambda$ is much
        smaller than the radius $R$ of the cylinder.
        {\bf Hint:}
-       Use the relation $I_c=\int_0^R dr \int_0^{2\pi} d\phi \, j_c(r)$
+       Use the relation $I_c=\int_0^R dr \int_0^{2\pi} d\phi \, j_c(r) r$
        and integration by parts.
- \item Calculate $j_c(R,T=0K)$ for a wire of Sn with a radius of 1 mm at $T=0K$.
+ \item Calculate $j_c(R,T=0K)$ for a wire of Sn with a diameter of 1 mm
+       at $T=0K$.
        The critical current and penetration depth at $T=0K$  are
        $I_c=75\, A$ and $\lambda =300\cdot 10^{-10}\, m$.
 \end{enumerate}
@@ -66,7 +67,7 @@ and $\lambda$ is the London penetration depth.
 \section{Penetration of the magnetic field into a type 1 superconductor}
 In the following, the behaviour of the magnetic field ${\bf B}_s({\bf r})$
 in the surface layer of a superconductor is calculated.
-In the superconductor the magnetic field is given by
+Inside the superconductor the magnetic field is given by
 \[
  {\bf B}_s=\mu_0 \left({\bf H}_a + {\bf M}_s\right)
 \]
@@ -82,7 +83,9 @@ ${\bf M}_s$ is the magnetization of the superconductor.
        magnetic field inside the superconductor?
        Apply the second London equation
        $\nabla \times {\bf j}_s=-{\bf B}_s/\Lambda$
+       with $\lambda=\sqrt{\Lambda/\mu_0}$
        relating the supercurrent to the magnetic field.
+       
  \item Consider a superconducting half space. The interface of the
        superconductor ($x>0$) and the vacuum ($x<0$) is located at $x=0$.
        A magnetic field ${\bf B}_a=\mu_0 H_a {\bf e}_z$
@@ -90,7 +93,7 @@ ${\bf M}_s$ is the magnetization of the superconductor.
        Calculate and sketch the decay of
        ${\bf B}_s=B_{s_z}(x) {\bf e}_x$
        in the superconductor.
-       Introduce the London penetration depth $\lambda=\sqrt{\Lambda/\mu_0}$.
+       Introduce the London penetration depth $\lambda$.
  \item Out of this, calculate the screening current density ${\bf j}_s$.
        What is the direction of the current?
        Calculate the value of ${\bf j}_s$ at the interface?