6. Consider the cyclotron setup below. We supply external fields: static magnetic field Bo and oscillating electric field Eo. The particle has charge qo, mass mo, and initial vertical velocity

vo. Because of the influence of Bo and Eo, the particle's speed and direction will change over time. The particle will spend less time in the E field as it gets faster. Please ignore this effect for this problem.Instead, assume the time is the same for mathematical simplicity. (a) Plot the velocity magnitude and phase through the B and E fields as a function of time t. Label values whenever the particle moves from an E field to a B field. For the phase, you are free to consider modulus, i.e. subtract multiples of 2n, if desired. (Two plots) (b) Suppose we make the magnetic field stronger, say 3Bo. Does the particle complete a B field half loop any faster than before? (Short answer) (c) Suppose the cyclotron has a maximum radius of rmax. What is the corresponding maximum velocity an electron can reach in this cyclotron? (Short answer)