\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
\[
{\bf B}_s=\mu_0 \left({\bf H}_a + {\bf M}_s\right)
\]
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 ${\bf B}_a=\mu_0 H_a {\bf e}_z$
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?