The Thomson experiment. An electron beam traverses a region of uniform electric field inside capacitor plates with the length l along the beam axis and separation d between the plates. The electron velocity vx is constant along the direction of the beam, before and after entering the capacitor. The electron velocity along the direction of the electric field is zero before entering the capacitor and vy after exiting. There is no magnetic field. a) Find the deflection angle of the electron beam after exiting the capacitor in terms of vx and vy . b) Find vy in terms of vx, d, the voltage V across the capacitor plates, and fundamental constants. (Don't just copy the equation out of the text - please show how to derive it). Now suppose that a uniform magnetic field of strength B is applied in a direction perpendicular to both the electric field and the beam direction. The direction and magnitude of B are such that there is no net force on an electron. c) Sketch the directions of E, B and the beam direction. Take into account the negative charge of the electron. d) Find the magnitude of B in terms of the given properties of the setup, vx, and fundamental constants