A charged particle starts from rest at the origin of ooordinates in a region where there is a uniform electric field E parallel to the x-axis, and a uniform magnetic flux density B parallel to the z-axis. Show that the coordinates of the particle at a time t later will be
x = (E / w*B) (1 cos(wt),
y = f(E / w*B)(wt sin wt),
z = 0,
where w = eB/m. (E = |E|, B = |B|)(This path is called a cycloid.)