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

A. `B=(2pi m v)/(e ) " and " K=2mpi^(2)v^(2)R^(2)`
B. `B=(mv)/(e ) " and " K=m^(2) pi v R^(2)`
C. `B=(mv)/(e ) " and " K=2m pi^(2) v^(2)R`
D. `B=(2pi m v)/(e ) " and " K=m^(2) pi v R^(2)`

Answer

A

Explanation

Frequency `upsilon-(eB)/(2pi m) " so " B=(2pi m v)/(e )`
Kinetic energy `K=(1)/(2)m v^(2)`
radius `R=(m v)/(e B)`