As shown in figure, uniform magnetic field between two identical plates is B . There is a hole in pl

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4.Moving Charges and Magnetism

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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

A

$B > \frac{{2mE}}{{qd}}$

B

$B > \frac{{\sqrt {2mE} }}{{qd}}$

C

$B < \frac{{2mE}}{{qd}}$

D

$B < \frac{{\sqrt {2mE} }}{{qd}}$

Solution

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

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

Standard 12

Physics

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