Question

A particle of mass $m$ abd 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

• A. $\frac{q(b-a)B}{m}$
• B. $\frac{q(b+a)B}{m}$
• C. $\frac{qaB}{m}$
• D. $\frac{qbB}{m}$

Answer 1

The correct option is A $\frac{q(b-a)B}{m}$

We know that , $R=\frac{mv}{Bq}$

If particle just enters $x>b$,

$R\ge (b-a)$

$\frac{mv}{Bq}\ge (b-a)$

$\Rightarrow v\ge \frac{Bq(b-a)}{m}$

$\therefore v_{min}=\frac{q(b-a)B}{m}$