Energy inside a cyclotron, and the frequency of circular motion

AI Thread Summary
The discussion focuses on calculating the maximal energy of protons and the frequency of their circular motion in a cyclotron with a 28 cm diameter and a magnetic field of 1.4 T. The kinetic energy formula used yields a result of approximately 1.1786 x 10^-12 J for the protons. The frequency of circular motion is calculated to be about 1.34059 x 10^8 rad/s. A clarification was made regarding the radius, confirming it should be half of the diameter. The calculations and understanding of the problem were affirmed after correcting the radius error.
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Homework Statement


One of the first cyclotrons, built in 1932, has D-s with a diameter of 28 cm, and its magnet was capable of producing magnetic field of 1.4 T. What is the maximal energy of the protons accelerated by this cyclotron? What is the frequency of the circular motion?

Homework Equations


A) Ek = (q2B2R2)/2m
B) ω = V / r, or qB / m

The Attempt at a Solution


A) ((1.602 X 10-19)2 X 1.42T X 0.282m)/(2 X 1.673 X 10-27kg) = 1.1786 X 10-12 J

B) (1.602 X 10-19 X 1.4T) / 1.673 X 10-27kg = 1.34059 X 108 rad/s

That make sense to your guys?
 
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Shouldn't the radius be half of the diameter?
 
gneill said:
Shouldn't the radius be half of the diameter?

Oh you're right! Read the problem too fast there!
 

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