An electron moves in a force field due to a uniform electric field E and a uniform magnetic field B that is at right angles to E. Let E = jE and B = kB. Take the initial position of the electron at the origin with initial velocity vo = ivo in the x direction. Find the resulting motion of the particle. Show that the path of motion is a cycloid.

x = a sin ωt + bt
y = a (1 - cos ωt)
z = 0

Cycloidal mtion of electrons is used in an electronic tube called a magnetron to produce the microwavesin a microwave oven.