Question

A charged particle of specific charge α moves with a velocity v = $v_{0}i$ in a magnetic field $\overrightarrow{B}=\frac{B_0}{\sqrt{2}}(\hat{j}+\hat{k})$. Then the (specific charge = charge per unit mass)

• A. path of the particle is a helix
• B. path of the particle is a parabola
• C. distance moved by the particle in time $t=\frac{\pi }{B_0\alpha }$ is $\frac{\pi v_0}{B_0\alpha }$
  
• D. velocity of the particle after time $t=\frac{\pi }{B_0\alpha }$ is $(\frac{v_0}{2}\hat{i}+\frac{v_0}{2}\hat{j})$

Answer 1

The correct option is C

distance moved by the particle in time $t=\frac{\pi }{B_0\alpha }$ is $\frac{\pi v_0}{B_0\alpha }$

$\overrightarrow{V}\perp \overrightarrow{B}$
Therefore, path of the particle is a circle, In magnetic field, speed of the particle remains constant. Therefore, distance moved by the particle in time. $t=\frac{\pi }{B_0\alpha }$ is $v_{0}t$ or $\frac{\pi v_0}{B_0\alpha }$