A cyclotron outputs a 5.0 (iA proton beam, with each charged particle having 20

Question

A cyclotron outputs a 5.0 (iA proton beam, with each charged particle having 20 MeV of kinetic energy. The cyclotron is comprised of two pairs of "D" shaped halves called "Dees", separated by a small gap which is switched with an electrical potential of 20 keV. The magnetic field between the upper and lower half of each of the "Dees" is 5 T. As the beam leaves the cyclotron, the protons strike and come to rest inside a target made from 50 grams of copper. What is the final speed of each proton upon exiting the cyclotron? What is the minimum radius of the cyclotron chamber? What is the period of rotation of the protons? How many times does each particle circle before exiting the apparatus? After exiting the cyclotron, how many particles strike the copper target in one second? What is the total momentum delivered to the target in one second? Using that momentum, estimate the force applied to the target. [Hint: use unit-analysis.] How much energy is deposited inside the target in one second? [Answer in Joules, please.] Assuming that all of that energy goes towards heating the copper target, how much time elapses before the temperature of the target rises by 300 Kelvins? If the cyclotron runs at 5% efficiency, how much power must be supplied to the machine to keep it running? The cyclotron takes its energy from a 400V industrial line. How much current does it draw?

Explanation / Answer

a. K=0.5^m*v2

20*1.6*10-13=0.5*1.67*10-27*v^2

v= 61.9*106 m/s

b. r=mv/qB

r=1.67*10-27*61.9*106 / (1.6*10-19*5)

r=0.13 mts

c. t= pi*m/(q*B)

t= 6.55*10-9 sec

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