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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
Options
a straight line
a circle
a helix with uniform pitch
a helix with non-uniform pitch
Solution
helix with uniform pitch
From the figure, the velocity of the particle can be resolved in two components,Vcosc parallel to the magnetic field and Vsin θ 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.
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