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Question

A non-relativistic positive charge particle of charge q and mass m is projected perpendicular to uniform magnetic field B as shown. Neglecting gravity, calculate xcoordinate of point on screen at which the charge particle will hit : d=R32, where R=mVqB


A
3R
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B
2R
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C
The particle describes a helical path of radius R=mvsinαqB
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D
The particle describes a circular path of radius R=mvqB
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Solution

The correct option is D The particle describes a circular path of radius R=mvqB
Since it is given that motion of the charged particle is perpendicular to the magnetic field, the particle describes a circular path of radius, R=mVqB
From figure,
sinθ=dR=32
θ=60
The required x coordinate where the charge will hit is
x=(RRcosθ)+dcot30
x=R2+R32×3=2R

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