Question

A particle moves in a region with a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the particle is perpendicular to the field direction. The path of the particle will be
(a) a straight line
(b) a circle
(c) a helix with uniform pitch
(d) a helix with non-uniform pitch

Answer 1

(d) a helix with non-uniform pitch

Here, the total Lorentz force on the particle,

F = qE + qVB

We all know that magnetic field B does not change the speed of the particle but changes its direction. But as an electric field is also present that accelerate the particle in the direction of the field, the resultant path is a helix with a non-uniform pitch.