An alternating electric field, of frequency v, is applied across the dees (radius = R) of a cyclotron that is being used to accelerated 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

Question

( A ) $B=\frac{2\pi mv}{e} and \; K=m^2\pi vR^2$
( B ) $B=\frac{2\pi mv}{e} and \; K=2m\pi^2v^2R^2$
( C ) $B=\frac{ mv}{e} and \; K=2m\pi ^2v^2R$
( D ) $B=\frac{ mv}{e} and \; K=m^2\pi vR^2$