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Question

As shown in the figure the uniform magnetic field between the two identical plates is B. There is a hole in the plate, If through this hole a particle of charge q, mass m and kinetic energy E enters the magnetic field, then the particle will not collide with the upper plate provided :

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A
B>2mEqd
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B
B>2mEqd
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C
B<2mEqd
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D
B<2mEqd
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Solution

The correct option is B B>2mEqd
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=mv2r
r=mvqB
Since r<d, mvqB<d
B>mvqd=m2Emqd=2mEqd

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