# A particle of specific charge q/m = π C kg-1 is projected from the origin toward positive x-axis with a velocity of …..

Q. A particle of specific charge $\displaystyle \frac {q}{m} = \pi$ C kg-1 is projected from the origin toward positive x-axis with a velocity of 10ms-1 in a uniform magnetic field $\vec B = -2\hat{k}T$ . The velocity $\vec v$ of the particle after time t=1/12 sec will be (in ms-1)

(a) $\displaystyle 5[\hat{i} + \sqrt 3 \hat{j}]$

(b) $\displaystyle 5[\sqrt 3 \hat{i} + \hat{j}]$

(c) $\displaystyle 5[\sqrt 3 \hat{i} – \hat{j}]$

(d) $\displaystyle 5[\hat{i} + \hat{j}]$

Ans: (b)
Sol: Time period of particle is

$\displaystyle T = \frac{2\pi m}{q B}$

$\displaystyle T = \frac{2\pi}{(q/m) B}$

$\displaystyle T = \frac{2\pi }{\pi \times 2} = 1 s$

after 1/12 sec , θ = 360°/12 = 30°

$\displaystyle \vec{v} = 10 cos30\hat{i}+ 10sin30\hat{j}$

$\displaystyle \vec{v} = 10 (cos30\hat{i}+ sin30\hat{j})$

$\displaystyle \vec{v} = 10 (\frac{\sqrt{3}}{2}\hat{i}+ \frac{1}{2}\hat{j})$

$\displaystyle \vec{v} = 5 (\sqrt{3}\hat{i}+ \hat{j})$