An electron (charge -e) moves in a constant electric field e along the r-axis and a constant magnetic field b along the z-axis. the initial velocity vo of the electron is in the xy-plane z =0 (a) write down the equations of motion in cartesian coordinates. (b) solve the equations of motion. (c) by eliminating time from the solution in b) show that the trajectory of the electron could be viewed as a circle of radius whose center drifts in the negative y-direction with a constant speed e/b (d) use your result in (b) to show that the charges with the same charge/mass ratio (i. e. the same w) and with the identical initial position a(0), y(0), z(0) will end up at the same spot in the xy-plane after one period t = 2π/w regardless of their initial velocities in the ry-plane, thereby demonstrating the charge-focusing ability of crossed constant electric and magnetic field (e) assuming 2 (0)=0, y(0)=0,刘0-0, and y(0) 50, use some graphics package to plot the trajectory of the charge from t-0 to t = 2π/w. (you might want to take that y(0)/w =1 and e/(ub) =1.)