Question

A particle with a specific charge $s$ is fired with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. What minimum magnetic field must exist in this region for the particle to not to hit the wall?

• A. $\frac{v}{sd}$
• B. $\frac{2v}{sd}$
• C. $\frac{v}{2sd}$
• D. $\frac{v}{4s}$

Answer 1

The correct option is A $\frac{v}{sd}$

Let us try to understand this problem with the help of this diagram

Let $r$ be the radius of this circular path.
So, $r\le d$
We know that $r=\frac{mv}{qB}$
$⟹\frac{mv}{qB}\le d$
$s$ (specific charge) $=\frac{q}{m}$
So, $\frac{v}{sB}\le d$
$⟹\frac{v}{sd}\le B$
Thus, the minimum value of $B=\frac{v}{sd}$