@@ -139,8 +139,8 @@ We apply a magnetic field $\bf B$ perpendicular to a planar (two-dimensional) sa
### Exercise 2: 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. Write down the Newton's equation of motion for the electron, compute $\frac{d\mathbf{v}}{{dt}}$.
1. Write down the Newton's equation of motion for the electron, compute $\frac{d\mathbf{v}}{{dt}}$.
2. 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.
3. Now we accelerate the electron by adding an electric $\mathbf{E}$ that is perpendicular to ${\bf B}$. Sketch the motion of the electron.
4. Adjust the differential equation for $\frac{d\mathbf{v}}{{dt}}$ found in (2) to include ${\bf E}$.
5. We now consider an electron in a metal. Include the Drude scattering time $\tau$ into the differential equation for the velocity you formulated in 4.
