Cycloid motion of a charged particle.

[Samson4]

Does the cycloid motion of the picture only apply to a particle at rest in the x y and z axis? What if it is moving with a velocity parallel to the magnetic field before the electric field accelerates it? I think it will then move in a spiral; although, I am not sure.

 

[Chandra Prayaga]

Does the cycloid motion of the picture only apply to a particle at rest in the x y and z axis? What if it is moving with a velocity parallel to the magnetic field before the electric field accelerates it? I think it will then move in a spiral; although, I am not sure.

View attachment 98159

With your configuration of the electric and magnetic fields, neither of them changes the y-component of the velocity. so as the particle moves along the cycloid, it also keeps moving along the y-direction with constant velocity.