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  4. 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?

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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?

Moving Charges and Magnetism

Solution:

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