A point charge q with mass m is released from rest at the origin in an external magnetic field and an external electric field. Both external fields are uniform (constant in magnitude and direction). The electric field is in the z direction and the magnetic field is in the x direction: E= Eoz, B= Box

where Eo and Bo are constants. The electric field will accelerate the point charge. Once the point charge has acquired a non-zero velocity it will experience a magnetic force as well. Using Newton's second law and the Lorentz force law, show that the motion of the point charge must obey the following equations:

d^2x/dt^2= 0, d^2y/dt^2= ωdz/dt, d^2z/dt^2= ω(Eo/Bo- dy/dt)

where ω is the cyclotron frequency.

ω= qBo/m