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

Answer 1

Answer: (A), (B)

The component of velocity $v$ along the direction of $B$ is $v\cos \theta$.
Since the trajectory will be helical, the trajectory will never be perpendicular to the direction of magnetic field $B$, it's trajectory will be inclined at a small angle to the direction of the magnetic field.
It will also never move parallel to $x-$axis.