@@ -96,9 +96,9 @@ We apply a magnetic field $\bf B$ perpendicular to a planar (two-dimensional) sa
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 accelerate the electron by adding an electric ${\bfE}$ that is perpendicular to ${\bf B}$. Sketch the motion of the electron.
4. Adjust the differential equation found in (2) to include ${\bf E}$.
2.Write down the Newton's equation of motion of the electron, compute $d\mathbf{v}{dt}$.
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 $d\mathbf{v}{dt}$ 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.
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?
