A cyclotron is designed to accelerate protons (mass 1.67 × 10⁻²⁷ kg) up to a kinetic energy of 2.5 × 10⁻¹³ J. If the radius of the dipole magnets is 96 cm, what is the magnetic field used in the cyclotron?

Question

Quizplus · Accepted Answer

The magnetic field B in a cyclotron is given by the formula B = (2 * KE) / (q * r^2), where KE is the kinetic energy, q is the charge of the proton (1.6 × 10^-19 C), and r is the radius in meters. Substituting the given values, B = (2 * 2.5 × 10^-13 J) / (1.6 × 10^-19 C * (0.96 m)^2) ≈ 0.19 T.

A Cyclotron Is Designed to Accelerate Protons (Mass 1