The region between y = 0 and y = d contains a magnetic field B = B z A particle of mass m and charge q enters the region with a velocity v = v i. If d = mv 2qB, the acceleration of the charged particle at the point of its emergence at the other side is

(A) \frac{{qvB}}{m}\,\left( {\,\frac{{ \hat j + \hat i}}{{\sqrt 2 }}} \right)

(B) \frac{{qvB}}{m}{\mkern 1mu} \left( {{\mkern 1mu} \frac{{\sqrt 3 }}{2}{\mkern 1mu} \hat i + \frac{1}{2}\hat j} \right)

(C) \frac{{qvB}}{m}\,\left( {\,\frac{{ - \hat j + \hat i}}{{\sqrt 2 }}} \right)

JEE Mains · Physics · STD 12 - Moving charges and magnetism

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

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Correct Answer

(D) \(\frac{{qvB}}{m}{\mkern 1mu} \left( {\frac{1}{2}\hat j - \frac{{\sqrt 3 }}{2}\hat i} \right)\)

Detailed explanation

\(\overrightarrow{\mathrm{B}}=\mathrm{B} \hat{\mathrm{k}}\)

\(r=\frac{m v}{q B}\)

\(r=2 d\)

\(\sin \theta=\frac{d}{2 d} \Rightarrow \sin \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{6}\)

\(\vec{a}=\frac{|q| v b}{m}(\cos \theta(-\hat{i})+\sin \theta \hat{j})\)

\(\vec{a}=\frac{|q| v b}{m}\left(-\frac{\sqrt{3}}{2} i+\frac{1}{2} \hat{j}\right)\)

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