Consider a positive charge q that is released from rest at the origin in the orthogonal uniform electric and magnetic fields E = E yˆ and B = B zˆ.
(i) Determine the full trajectory, i.e. x(t) and y(t), and show that the trajectory is a cycloid curve.
(ii) What is the average velocity in the x and the y-direction?
(iii) Plot the kinetic energy as a function of time.