Question 162 of 276

The region between $y=0$ and $y=\mathrm{d}$ contains a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B} \hat{\mathrm{z}}$. A particle of mass $\mathrm{m}$ and charge $\mathrm{q}$ enters

the region with a velocity $\vec{v}=v \hat{i} .$ if $\mathrm{d}=\frac{\mathrm{m} v}{2 \mathrm{qB}},$ the acceleration of the charged particle at the point of its emergence at the other side is :

A$\frac{\mathrm{q} v \mathrm{~B}}{\mathrm{~m}}\left(\frac{1}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j}\right)$B$\frac{\mathrm{q} v \mathrm{~B}}{\mathrm{~m}}\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right)$C$\frac{\mathrm{q} v \mathrm{~B}}{\mathrm{~m}}\left(\frac{-\hat{j}+\hat{i}}{\sqrt{2}}\right)$DNone of the above

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Answer: (D) None of the above

Assuming particle enters from $(0, \mathrm{~d})$

$r=\frac{m v}{q B}, \quad d=\frac{r}{2}$




$a=\frac{q V B}{m}\left[\frac{-\sqrt{3} i-j}{2}\right]$

this option is not given in the all above four choices.