Question

A charged particle moves in a uniform magnetic field. The velocity of the particle at some instant makes an acute angle with the magnetic field. 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) helix with uniform pitch

From the figure, the velocity of the particle can be resolved in two components,Vcos$\theta$ parallel to the magnetic field and Vsin $\theta$ perpendicular to the magnetic field. We know that magnetic field does not change the speed of a particle; rather, it changes the direction of its velocity. So, a magnetic force acts on the particle due to the vertical component of velocity, which tries to move the particle in a circle.This force tries to rotate the particle in a circle. But as there is a horizontal component of velocity also, the particle will move helically with a constant pitch because no force acts on the particle along the direction of the horizontal component of velocity.