An alternating electric field of frequency v , is applied across the dees (radius = R ) of a cyclotron that is being used to accelerate protons (mass = m ). The operating magnetic field ( B ) used in

Question

An alternating electric field of frequency v , is applied across the dees (radius = R ) of a cyclotron that is being used to accelerate protons (mass = m ). The operating magnetic field ( B ) used in the cyclotron and the kinetic energy ( K ) of the proton beam, produced by it, are given byNEET 2012 (Screening)

TestHub · Accepted Answer

Frequency v = 2 πm e B ​ KE = 2 1 ​ m v 2 and radius R = e B m v ​ Here, velocity v = T /2 π R ​ = T 2 π R ​ = 2 π R v ∴ Radius R = e B m ( 2 π R v ) ​ Magnetic field B = e 2 πm v ​ Kinetic energy K = 2 1 ​ m ( 2 π R v ) 2 = 2 m π 2 v 2 R 2

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