A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x b$ is

Question

A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is

Dr. Abubacker · Accepted Answer

(b) In the figure, the $z$-axis points out of the paper, and the magnetic field is directed into the paper, existing in the region between $PQ$ and $RS$. The particle moves in a circular path of radius $r$ in the magnetic field. It can just enter the region $x > b$ for $r \geq (b - a)$
Now, $r = \frac{mv}{qB} \geq (b - a)$
Or $v \geq \frac{q(b - a)B}{m} \Rightarrow v_{\min} = \frac{q(b - a)B}{m}$

Explanation

Reviewed by Dr. Abubacker

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