Question

State under what conditions will a charged particle moving through a uniform magnetic field travel in (i) a circular path (ii) a helical path.

Answer 1

A charged particle travels in a circular path within a magnetic field `vec(B)`, if its velocity `vec(v)` is perpendicular to `vec(B)`. A charged particle travels in a helical path through a magnetic field `vec(B)`, if its velocity `vec(v)` is inclined at an angle θ to `vec(B)`, 0 < θ < 90°. In this case, the component of `vec(v)` parallel to `vec(B)` is unaffected by the magnetic field. The radius and pitch of the helix are determined respectively by the perpendicular and parallel components of `vec(v)`.