@@ -89,12 +89,14 @@ While most materials have $R_{\rm H}>0$, interestingly some materials are found
### Exercise 1: Motion of an electron in a magnetic and an electric field.
We first consider an electron in free space, moving in a plane perpendicular to a magnetic field ${\bf B}$ with velocity ${\bf v}$.
1. What is the shape of the motion of the electron? Calculate the characteristic frequency and time-period $T_c$ of this motion for $B=1$ Tesla.
2. Formulate a differential equation for ${\bf v}$.
3. Now we add an electric $E$ that is perpendicular to ${\bf B}$. Sketch the motion of the electron.
4. Adjust the differential equation of found in (2) to include ${\bf E}$.
We now consider an electron in a metal.
5. Drude theory assumes a scattering time $\tau$. Include this time into the differential equation for the velocity you formulated in 4.
6. Let's assume $\tau \gg T_c$. What would the shape of the motion of the electron be in this limit? What would the shape be when $\tau \ll T_c$? Which of these two limits holds in a typical metal?
