What happens if a charged particle is moving at an angle (neither parallel nor perpendicular) to the magnetic field B?
For example, in the diagram above, we have a uniform B-field directed in the +x direction. A positive charge q is moving at velocity v in the x–y plane, making an angle q with the x-axis.
The analysis becomes much easier if we make an astute decision to resolve the velocity into
- the component parallel to B, and
- the component perpendicular to B, .
If the charge had only velocity , it would have experienced zero magnetic force, since its velocity is completely parallel to the magnetic field. This charge would continue travelling forward (in the +x direction) at a constant velocity.
If the charge had only velocity , it would have experienced the centripetal magnetic force , since its velocity is perpendicular to the magnetic field. Its motion would have been circular motion of radius in the y-z plane.
Since the charge had both and , we have to superpose the two motions together. What we get is a circular motion of radius that moves forward at a constant speed . The resultant motion is a helical path, like a screw with a pitch of .