Question

A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the x-axis. During its motion along a helical path, the particle will

• A. Never move parallel to the x-axis.
• B. Move parallel to the x-axis once during every rotation for all values of $\theta$
• C. Move parallel to the x-axis at least once during every rotation if $\theta ={45}^{\circ }$.
• D. Never move perpendicular to the x-direction.

Answer 1

Answer: (A), (D)

Never move perpendicular to the x-direction.

Let us try to understand this with the help of diagram
The direction of magnetic force is into the paper.
Due to this force the charge particle will follow a hellical path.

So, this particle will never move parallel to $x$ axis.
From this we can easily depict that options (b) and (c) both are wrong.
Due to its hellical path , the circular motion of the particle during every rotation will be a bit tilted in forward direction, so it will never move perpendicular to $x$ axis.