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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Impulse imparted to bead is qRB2

Impulse imparted to bead is qRB

If q=4mBgR then bead will complete vertical circular motion

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

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