Solution:
The particle moves along a circle and returns to its original position after completing the circle that is after one time period. The time period is
If the velocity of the charge is not perpendicular to the magnetic field, we can break the velocity in two components- , parallel to the field and perpendicular to the field. The component remains unchanged as the force is perpendicular to it. In the plane perpendicular to the field, the particle traces a circle of radius as given by equation. The resultant path is a helix