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

Question

A particle with a specific charge s is fired with a speed v toward a wall at a distance d, perpendicular to the wall. What minimum magnetic field must exist in this region for the particle not to hit the wall? (A) v / s d (B) 2 v / s d (C) v / 2 s d (D) v / 4 s d

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/fe9ddd7e616bdefe8b5b377a439d78bf-.png" /> The particle moves in a circular path with radius d if it is to just miss the wall. ⇒ m v=B q r, r=d or B=(v/(q / m) d)=(v/s d)

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

$v / s d$

$2 v / s d$

$v /2 s d$

$v /4 s d$

The particle moves in a circular path with radius $d$ if it is to just miss the wall.
$\Rightarrow m v = Bq r, r = d$
or $B = \frac{v}{( q / m ) d} = \frac{v}{s d}$

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

v/sd

2v/sd

v/2sd

v/4sd