Question

A cyclotron for accelerating protons has a maximum radius of 0.700 m and has a magnetic field of 0.200 T.

(A) what is the cyclotron frequency?

(B)what is kinetic energy of the protons when they emerge?

Answer 1

(A) what is the cyclotron frequency?

$$f=\frac{1}{T}=\frac{qB}{2\pi m}$$ $$f=\frac{1.6*10^{-19}*0.150}{6.28*1.67*10^{-27}}=2.29*10^{6}\:\rm Hz$$

(B) what is the kinetic energy of the protons when they emerge?

$$E_k=\frac{mv^2}{2}=\frac{m(2\pi rf)^2}{2}$$ $$E_k=\frac{1.67*10^{-27}(2\pi *0.60*2.29*10^6)^2}{2}\\ =6.21*10^{-14}\:\rm J$$