As shown in the figure, the uniform magnetic field between the two identical plates is $B$. There is a hole in plate. If through this hole a particle of charge $q$, mass $m$ and energy $E$ enters this magnetic field, then the particle will not collide with the upper plate provided
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The particle will bend in the magnetic field.
The particle will not collide with the upper plate if radius of the semicircular trajectory is less than the distance $d$ between the plates.
Equating Lorentz force and centripetal force for circular motion,
$qvB =\frac{ mv ^2}{ r }$
$\therefore r =\frac{ mv }{ qB }$
Since $r < d , \frac{ mv }{ qB } < d$
$\therefore B > \frac{ mv }{ qd }=\frac{ m \sqrt{\frac{2 E }{ m }}}{ qd }=\frac{\sqrt{2 mE }}{ qd }$
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