Question

A charged particle of specific charge $\alpha$ enters in a magnetic field $\overrightarrow{B}=\frac{B_0}{\sqrt{2}}(\hat{j}+\hat{k})$ with a velocity $\overrightarrow{v}=v_0\hat{i}$. Then (specific charge = charge per unit mass)

Answer 1

Since $\overrightarrow{v}\perp \overrightarrow{B}$ , path of the particle must be circular.

In uniform magnetic field , speed of the particle remains constant.
$\therefore$ Distance travelled by particle in time $t=\frac{\pi }{B_0\alpha }$ is $d=v_0\times t$
$=v_0\times \left(\frac{\pi }{B_0\alpha }\right)$

Hence, options (b) and (c) are the correct answers.