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}] $
Click to See Answer :
$ \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}) $