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Q.

A charged particle (charge q, mass m) is placed at the centre of a circular region containing a magnetic field. The field is given as B=B(r) i.e; it is a function of radial distance and it is perpendicular to the plane of the circle. The total magnetic flux through the circle is zero. The particle is given a radial impulse. At a later instant the radial and tangential components of velocity of the particle are vr  and  vθ respectively.

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a

The tangential force on the particle at an instant is  qvθB(r)

b

The torque about centre on the particle is  qBrvr

c

If the particle leaves the circular region then at the instant it leaves, its velocity is only in radial direction

d

If the particle leaves the circular region then at the instant it leaves, its velocity is only in tangential direction

answer is B, C.

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Detailed Solution

ϕ=0B(r).2πrdr=0          rB(r)dr=0(1)       

Tangential force  =rBvr
Torque about centre =rqBvr
ΔL=τdt=qrBvrdt=qrBdt=0      (from  (1))       finally   vθ=0

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