Final answer:
A charged particle with velocity components both parallel and perpendicular to a magnetic field follows a helical path, with the perpendicular component causing circular motion and the parallel component moving the particle along the field.
Step-by-step explanation:
When a charged particle moves in a magnetic field with a velocity that has components both parallel and perpendicular to the field, the path of the particle will be a helix. The perpendicular component of the velocity causes the particle to execute a circular motion, due to the magnetic force acting as a centripetal force, which is always perpendicular to the velocity. This force does not change the speed of the particle, only its direction. Therefore, the motion in the plane perpendicular to the magnetic field is uniform circular motion. The parallel component, however, is unaffected by the magnetic field, so the particle also moves with a constant speed along the direction of the field. Combining these two motions results in a helical path.
The radius of the circular path is determined by the balance between the magnetic force and the centripetal force required to keep the particle in circular motion. The pitch of the helix - the distance along the field direction between successive turns of the spiral - is determined by the component of the velocity parallel to the magnetic field. Thus, the overall motion of the charged particle is akin to that of a screw moving through a surface).