Magnetic Effects Of Current Question 401
Question: A particle of specific charge $ \frac{q}{m}=\pi Ck{{g}^{-1}} $ is projected from the origin towards positive x-axis with a velocity of $ 10m{{s}^{-1}} $ in a uniform magnetic field $ \overset{\to }{\mathop{B}},=-2\hat{k},T $ . The velocity $ \overrightarrow{v} $ of particle after time = 1/12 s will be $ (in,m{{s}^{-1}}) $
Options:
A) $ 5[\hat{i}+\sqrt{3}\hat{j}] $
B) $ 5[\sqrt{3}\hat{i}+\hat{j}] $
C) $ 5[\sqrt{3\hat{i}}-\hat{j}] $
D) $ 5[\hat{i}-\hat{j}] $
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Answer:
Correct Answer: B
Solution:
[b] Time period, $ T=\frac{2\pi m}{qB}=\frac{2\pi }{\pi \times 2}=1s $ Thus, particle will be at point P after $ t=\frac{1}{12}s $ $ \overset{\to }{\mathop{v}},=10[ \cos ,30\hat{i}+\sin ,30\hat{j} ] $ $ \overset{\to }{\mathop{v}},=10[ \frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} ]=5[ \sqrt{3}\hat{i}+\hat{j} ]m{{s}^{-1}} $
BETA
