The diagram shows a circular non-conducting smooth fixed track kept concentric to a magnetic field of magnitude B which exists in a cylindrical region of radius r (r > R). There is small bead of mass m and charge q rests on the track. A bead can move freely along track. If the magnetic field is switched off then
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a
Impulse imparted to bead is qRB2
b
Impulse imparted to bead is qRB
c
If q=4mBgR then bead will complete vertical circular motion
d
If q=mBgRthen bead will complete vertical circular motion
answer is A.
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Detailed Solution
Sudden removal of magnetic field results in induced emf, which produces non conservative eletric field.This electric field applies impulsive force on charge.∮E→ .dr→=ξ=−dϕdt⇒E2πR=πR2dBdt⇒Edt=RdB2⇒ Impulse =∫Fdt=∫qEdt=∫qR2dB=qRB2⇒mv=qRB2⇒ Minimum velocity to complete a circle =4gR⇒q=2mvRB=2mRB4gR=4mBgR