4. Field transformations and electrodynamics: Consider a lab frame with constant and uniform fields of E = 82 V/m and B = -2ŷ T perpendicular to one another. Answer the following questions: a) If a point charge with q = 1 C is observed to be moving within the lab frame with some constant velocity v = vx, what would be vr? Hint: how about making sure that the electric field E' = 0 in the reference frame of the moving charge? Explain your reasoning carefully. b) Consider an electron with charge q = -1.6 × 10-19 C in motion in the lab frame such that at time t = 0 it appears to have a velocity of v' = 2 m/s within the moving frame of the first charge. What would be the acceleration of the electron at time t = 0? Hint: B' = B, F = ma, and the mass of the electron is m = 9.1 × 10-31 kg. c) Bonus problem - a nice challenge: Show that the electron mentioned in part (b) will follow a periodic circular trajectory within the primed reference frame as a function of time t. Hint: set up a differential equation starting with mdv'/dt = qv' x B where v' = dr'/dt and solve it subject to initial conditions, say, r' = 0 and v' = 2 m/s at t = 0.

Fig: 1