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# A uniform magnetic field $\overrightarrow B = B_0\hat j$ exists in space. A particle of mass $m$ and charge $q$ is projected towards negative $x$-axis with speed $v$ from a point $(d,0,0)$. The maximum value of $v$ for which the particle does not hit the $y-z$ plane is

$\begin {array} {1 1} (a)\;\large\frac{2Bq}{dm} & \quad (b)\;\large\frac{Bqd}{m} \\ (c)\;\large\frac{Bq}{2dm} & \quad (d)\;\large\frac{Bqd}{2m} \end {array}$

As the magnetic field is uniform, the question requires the following condition to be satisfied
$d = \large\frac{mv}{qB}$
$\Rightarrow v = \large\frac{Bqd}{m}$
Ans : (b)