Question #312745

A cyclotron for accelerating protons has a maximum radius of 0.600 m and has a magnetic field of 0.150 T.


(A) what is the cyclotron frequency?


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


Mass (m) proton = 1.67×10-²⁷kg


Charge (q) proton = 1.60×10-¹⁹C

1
Expert's answer
2022-03-16T18:28:36-0400

(A) what is the cyclotron frequency?

f=1T=qB2πmf=\frac{1}{T}=\frac{qB}{2\pi m}

f=1.610190.1506.281.671027=2.29106Hzf=\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?


Ek=mv22=m(2πrf)22E_k=\frac{mv^2}{2}=\frac{m(2\pi rf)^2}{2}

Ek=1.671027(2π0.602.29106)22=6.211014JE_k=\frac{1.67*10^{-27}(2\pi *0.60*2.29*10^6)^2}{2}\\ =6.21*10^{-14}\:\rm J


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