Halliday, Resnick & Walker — Magnetic Fields: Problem 65

65 An alpha particle can be produced in certain radioactive decays of nuclei and consists of two protons and two neutrons. The particle has a charge of \( q = +2e \) and a mass of \( 4.00 \text{ u} \), where \( \text{u} \) is the atomic mass unit, with \( 1 \text{ u} = 1.661 \times 10^{-27} \text{ kg} \). Suppose an alpha particle travels in a circular path of radius \( 4.50 \text{ cm} \) in a uniform magnetic field with \( B = 1.20 \text{ T} \). Calculate (a) its speed, (b) its period of revolution, (c) its kinetic energy, and (d) the potential difference through which it would have to be accelerated to achieve this energy. (e) If the field magnitude is doubled, what is the ratio of the new value of kinetic energy to the initial value?