1. Justify the definition of “cyclotron” frequency ω p =eB/m by showing that the solutions of the coupled x-and y-equations of motion in the absence of an E-field and without scattering (only Lorentz force) describe circular trajectories. 2. In the Drude model, scattering is inelastic, i.e. energy is lost. First, derive the energy lost per collision. Then, by averaging over the probability distribution of scattering times, g G ± ² ³ ´ , derive the power density lost to the ions by collisions. Show that this “Joule heating” is consistent with the geometry-dependent expression P=I 2 R. 3. Propagation of EM waves in metals a. We used a high-frequency approximation to the complex AC conductivity in the
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