A cyclotron is designed to accelerate singly–ionised ions (mass

PHYSICS · Subjective · ISC · Physics · Magnetic Effects of Current and Magnetism · Work, Energy and Power

Problem

A cyclotron is designed to accelerate singly–ionised 12C{}^{12}\text{C} ions (mass m=1.99×10−26 kgm = 1.99 \times 10^{-26}\,\text{kg}, charge q=1.60×10−19 Cq = 1.60 \times 10^{-19}\,\text{C}). The uniform magnetic field inside the dees has a magnitude of 1.8 T1.8\,\text{T}. (i) Calculate the frequency of the alternating voltage that must be applied between the dees so that the ions remain in resonance. (ii) If the dees have a maximum usable radius of 0.40 m0.40\,\text{m}, determine the kinetic energy (in MeV) with which the ions leave the cyclotron.

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