4. Consider the cyclotron setup below. We supply external fields: static magnetic field Bo and oscillating electric field E. The particle has charge |8q|, mass m, and initial vertical velocity vo. Because of the influence of B and E, the particle's speed and direction will change over time. The particle will spend less time in the 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 vertical and horizontal velocities through the B and E fields as a function of time t. Assume the starting position denotes the origin. Label values whenever the particle moves from an E field to a B field. (Two plots) E B +|8q[,m Vo X X E B E B KE x t t (b) Suppose you have a cyclotron configured for protons with a certain top speed vs given a certain D-ring radius and consistent B, E fields. If you want to reconfigure it to fire electrons at the same v+ without changing rf or the exit aperture position, how would you have to change the B, E field properties? (Relevant expressions)