Question

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

Answer 1

A charged particle follows a helical trajectory in a uniform magnetic field (B) if:

1. The external magnetic field must be constant in magnitude and direction.
2. The particle’s velocity (v) must have both perpendicular component (v_⊥) that generates circular motion around field lines and parallel component (v_{| |}) that causes uniform motion along the field.
3. The combination of circular motion and linear motion results in a helix.
4. The motion remains helical as long as no other external forces (like electric fields) act on the particle.