An electron moves in a force field due to a uniform electric field E and a uniform magneti...

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 v0 = iv0 in the x direction. Find the resulting motion of the particle. Show that the path of motion is a cycloid:

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