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Q.

A magnetic field B→=-B0i^exists within a sphere of radius R=v0T3 where T is the time period of one revolution of a charged particle starting its motion from origin and moving with a velocity v→0=v023i^-v02j^. Find the number of turns that the particle will take to come out of the magnetic field.

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answer is 2.

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Detailed Solution

v⊥=-v02 will contribute to circular motion.  v‖=v032 will contribute to helical path. T=2πmB0q  Pitch, P=v‖T=v032T  Number of turns =RP=v0T3(2)v03T=2
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