From e53bf68c01b1f2408f15dcc155ca0715fdf7aa20 Mon Sep 17 00:00:00 2001 From: hackbard Date: Thu, 26 Jun 2008 11:41:26 +0200 Subject: [PATCH] small fixes --- solid_state_physics/tutorial/2_01s.tex | 2 +- solid_state_physics/tutorial/2_02.tex | 3 ++- solid_state_physics/tutorial/2_02s.tex | 2 +- 3 files changed, 4 insertions(+), 3 deletions(-) diff --git a/solid_state_physics/tutorial/2_01s.tex b/solid_state_physics/tutorial/2_01s.tex index 22abb78..033c8ae 100644 --- a/solid_state_physics/tutorial/2_01s.tex +++ b/solid_state_physics/tutorial/2_01s.tex @@ -62,7 +62,7 @@ \item $I = (\textrm{charge}) \cdot (\textrm{loops per time}) \stackrel{1/T=\omega_L/2\pi}{=} (Ze)(\frac{1}{2\pi}\frac{-e}{2m}B)$\\ - $\mu=IA=I2\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\ + $\mu=IA=I\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\ $== \Rightarrow =3=3$\\ $<\rho^2>=+=\frac{2}{3}$\\ $\mu=-\frac{Ze^2B}{6m}$ diff --git a/solid_state_physics/tutorial/2_02.tex b/solid_state_physics/tutorial/2_02.tex index ecafd2a..b9b5c5a 100644 --- a/solid_state_physics/tutorial/2_02.tex +++ b/solid_state_physics/tutorial/2_02.tex @@ -58,7 +58,8 @@ and $\lambda$ is the London penetration depth. {\bf Hint:} 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} diff --git a/solid_state_physics/tutorial/2_02s.tex b/solid_state_physics/tutorial/2_02s.tex index 8c12196..8f3eda0 100644 --- a/solid_state_physics/tutorial/2_02s.tex +++ b/solid_state_physics/tutorial/2_02s.tex @@ -55,7 +55,7 @@ and $\lambda$: London penetration depth. \Rightarrow dr=\lambda dx$, $r=\lambda x$ $\Rightarrow I_c=j_c(R)2\pi \lambda^2 \exp(-R/\lambda) \int_0^R d(\frac{r}{\lambda}) - \, \frac{r}{\lambda} \exp(\frac{r}{\lambda})$ + \, \frac{r}{\lambda} \exp(\frac{r}{\lambda})$\\ Integration by parts: $\int uv' = uv - \int vu'$\\ $\int xe^x dx = xe^x-\int e^x dx=xe^x-e^x+c=e^x(x-1)+c$\\ $\Rightarrow -- 2.39.2