Question

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

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

Answer 1

Answer: (B), (C)

The correct options are
B distance moved by particle intime $t=\frac{\pi }{B_0\alpha }is\frac{\pi v_0}{B_0\alpha }$
C path of the particle is a circle

1) Path of particle in magnetic field is either circular, straight line or helix, Here charged particle is projected at an angle so path must be circular.
2)
$\overline{v}=v_0\overline{i}$
$\overline{F}=q(\overline{v}\times \overline{B})$
$\overline{F}=q(v_0\overline{i}\times \frac{B}{\sqrt{2}}(\overline{j}+\overline{k}\left)\right)$
$\overline{F}=q{v}_0\frac{B}{\sqrt{2}}(\overline{k}-\overline{j})$
Distance travelled by particle in time
$t=v\cdot t=v_0\cdot \frac{\pi }{B_0\alpha }$