NEET2012PhysicsMagnetic Effects of CurrentActual
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 by
Options
- AB= m v e and K=2 m ^2 v^2 R^2
- BB= 2 m v e and K=m^2 v R^2
- CB= 2 m v e and K=2 m ^2 v^2 R^2
- DB= m v e and K=m^2 v R^2
Correct answer
C. B= 2 m v e and K=2 m ^2 v^2 R^2
Step-by-step solution
Frequency v= e B 2 m KE = 1 2 m v^2 and radius R= m v e B Here, velocity v= R T / 2 = 2 R T =2 R v Radius R= m(2 R v) e B Magnetic field B= 2 m v e Kinetic energy K= 1 2 m(2 R v)^2=2 m ^2 v^2 R^2