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 is given by the formula K = qVB, where q is the charge of the proton, V is the potential difference across the accelerator, and B is the magnetic field. Since the charge and potential difference are constant, the maximum kinetic energy is directly proportional to the magnetic field. When the magnetic field is increased from 1.2 T to 1.5 T, the maximum kinetic energy will increase as well. The ratio of the maximum kinetic energies is given by (1.5/1.2)^2, which is approximately 1.56. This means that the maximum kinetic energy increases by 56%. Therefore, the correct answer is (C) It increases by 56%.

A Cyclotron Is Designed with a Magnet That Produces a Magnetic