Question

Explain the necessary conditions in which the trajectory of a charged particle is helical in a uniform magnetic field.

Hint:

For a helical trajectory, a charged particle must have both a perpendicular and a parallel component of velocity with respect to the magnetic field.

Answer 1

A charged particle traversing a uniform magnetic field follows a helical path when its velocity possesses both parallel and perpendicular components relative to the field. - The magnetic force, acting perpendicularly to the particle's velocity, induces circular motion within the plane orthogonal to the magnetic field. - The velocity component aligned with the magnetic field dictates the particle's movement along the field's direction. Consequently, the particle's trajectory is a spiral (helical) path, where the magnetic force supplies the centripetal force for the circular component, and the parallel velocity component propels the particle along the field's axis.