An alternating electric field, of frequency $v$, is applied across the dees (radius $=R$ ) of a cycl

Question

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\

Professor PC Thomas Classes · Answer

(c): Frequency, $v=\frac{e B}{2 \pi m}$ or $B=\frac{2 \pi m v}{e}$ As $\frac{m v^{2}}{R}=e v B$ or $\quad v=\frac{e B R}{m}=2 \pi v R$\ Kinetic energy, $K=\frac{1}{2} m v^{2}=\frac{1}{2} m(2 \pi v R)^{2}=2 m \pi^{2} v^{2} R^{2}$\