Particle accelerators: A cyclotron is designed with a magnet that produces a magnetic field of 1.2 T. When refurbished, the magnet is replaced by one that produces a 1.5-T field. How does the maximum kinetic energy achieved by the protons change compared to their previous maximum kinetic energy?
A) It increases by 25%.
B) It decreases by 25%.
C) It increases by 56%.
D) It decreases by 56%.
E) It does not change.

Question

Quizplus · Accepted Answer

The maximum kinetic energy of the protons in a cyclotron is given by the equation:

K_max = qV_maxr

where q is the charge of the particle, V_max is the maximum potential difference applied to the dees, and r is the radius of the dees. The maximum potential difference in a cyclotron is given by:

V_max = Bf r^2 / (2m)

where B is the magnetic field strength, f is the frequency of the alternating voltage applied to the dees, and m is the mass of the particle.

Since the radius of the dees and the frequency of the alternating voltage remain constant, we can see that the maximum kinetic energy is proportional to the magnetic field strength. Therefore, increasing the magnetic field strength from 1.2 T to 1.5 T will increase the maximum kinetic energy by:

(K_max,new - K_max,old) / K_max,old x 100%
= [(1.5 / 1.2)^2 - 1] x 100%
= 56.25%

Therefore, the maximum kinetic energy achieved by the protons increases by 56%. The correct answer is C).

Particle Accelerators: a Cyclotron Is Designed with a Magnet That