MHT CET2018PhysicsMagnetic Effects of Current
An alternating electric field of frequency f is applied across the radius R of a cyclotron to accelerate protons (mass m ). The operating magnetic field B used and K.E. of the proton beam produced by it are respectively ( e = charge on proton)
Options
- A2 π m f e , 2 π 2 m f 2 R 2
- B2 π 2 m f e 2 , 4 π 2 m f 2 R 2
- Cπ m f e , π 2 m f 2 R 2
- D2 π 2 m 2 f 2 e , 2 π 2 m 2 f 2 R 2
Correct answer
A. 2 π m f e , 2 π 2 m f 2 R 2
Step-by-step solution
T = 2 π m e B R = m f e B = P e B B = 2 π m e f P = e B R = e × 2 π m υ e R K . E = P 2 2 m = ( 2 π m f R ) 2 2 m = 2 π 2 m f 2 R 2