Question

A proton is fired from origin with velocity $\overrightarrow{v}=v_0\hat{j}+v_0\hat{k}$ in a uniform magnetic field $\overrightarrow{B}=B_0\hat{j}$ (Take $m=$mass and $q=$ charge). Path of the proton particle is

• A. A helix with non-uniform pitch
• B. A circle
• C. A straight line
• D. A helix with uniform pitch

Answer 1

The correct option is D A helix with uniform pitch

The diagram for the given values,


Velocity $\overrightarrow{v}$makes an angle of ${45}^{\circ }$
with the magnetic field $\overrightarrow{B}$.

So, its path will be helix , due to $x-$component of velocity of particle will describe circular motion and due to $y-$component of velocity of it, will move forward.

Since the magnetic field is uniform, there will not be any magnetic force along $y-$axis. So it will move with uniform pitch.

Hence, option (c) is the correct answer.