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

For a charged particle moving in a uniform magnetic field, the trajectory will be helical if there is a component of velocity parallel to the magnetic field, as well as a perpendicular component. - The magnetic force acts perpendicular to the velocity, causing the particle to move in a circular path in the plane perpendicular to the magnetic field. - The component of the velocity parallel to the magnetic field causes the particle to move along the direction of the magnetic field. Thus, the particle moves in a spiral (helical) path, with the magnetic force providing the centripetal force for circular motion, while the parallel velocity component moves the particle along the field direction.