JEE PYQ: Magnetic Effects Of Current Question 48
Question 48 - 2019 (11 Jan 2019 Shift 2)
The region between $y = 0$ and $y = d$ contains a magnetic field $\vec{B} = B\hat{z}$. A particle of mass $m$ and charge $q$ enters the region with a velocity $\vec{v} = v\hat{i}$. If $d = \frac{mv}{2qB}$, the acceleration of the charged particle at the point of its emergence at the other side is:
(1) $\frac{qvB}{m}\left(\frac{1}{2}\hat{i} - \frac{\sqrt{3}}{2}\hat{j}\right)$
(2) $\frac{qvB}{m}\left(\frac{\sqrt{3}}{2}\hat{i} + \frac{1}{2}\hat{j}\right)$
(3) $\frac{qvB}{m}\left(\frac{-\hat{j} + \hat{i}}{\sqrt{2}}\right)$
(4) $\frac{qvB}{m}\left(\frac{-\sqrt{3}\hat{i} - \hat{j}}{2}\right)$
Show Answer
Answer: (4) $\frac{qvB}{m}\left(\frac{-\sqrt{3}\hat{i} - \hat{j}}{2}\right)$
Solution
$d = r/2$, $\sin\theta = 1/2$, $\theta = 30°$. Acceleration at emergence: $\vec{a} = \frac{qvB}{m}\left(\frac{-\sqrt{3}\hat{i} - \hat{j}}{2}\right)$.
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