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

• A

  $B=\frac{m v}{e}$ and $K=2 m \pi^2 v^2 R^2$
• B

  $B=\frac{2 \pi m v}{e}$ and $K=m^2 \pi v R^2$
• Correct answer
  C

  $B=\frac{2 \pi m v}{e}$ and $K=2 m \pi^2 v^2 R^2$
• D

  $B=\frac{m v}{e}$ and $K=m^2 \pi v R^2$

Hence, the correct answer is option: 'C'.