A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin shown in Fig. There is a uniform electric field E in the +y-direction and a uniform magnetic field B directed out of the page. It is shown in more advanced books that the path is a cycloid whose radius of curvature at the top points is twice the y-coordinate at that level.
(a) Explain why the path has this general shape and why it is repetitive. (b) Prove that the speed at any point is equal to √2qEy/m.

(c) Applying Newton's second law at the top point and taking as given that the radius of curvature here equals 2y; prove that the speed at this point is 2E/B.