Consider a particle of mass m and charge q moving in the presence of constant and uniform

Question:

Consider a particle of mass m and charge q moving in the presence of constant and uniform electromagnetic fields given by E = E_oŷ and B = B_oẑ. Assuming that initially (t = 0) the particle is at rest at the origin of a Cartesian coordinate system, show that it moves on the cycloid

Plot the trajectory of the particle in the z = 0 plane for q > 0 and for q ⊥ > V_E, V_⊥ = V_E, and V_⊥ E, where v_⊥ denotes the particle cyclotron motion velocity and v_E is the electromagnetic drift velocity.