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 $r < d , \frac{ mv }{ qB } < d$

$\therefore B > \frac{ mv }{ qd }=\frac{ m \sqrt{\frac{2 E }{ m }}}{ qd }=\frac{\sqrt{2 mE }}{ qd }$