A beam of alpha particles (each of mass 6.64×10−27kg and charge +2e) is sent into a region containing a uniform magnetic field such that the particles describe a circular path of radius 0.125m. Each alpha particle enters the field with a speed of 1.5×106ms−1, and its velocity is perpendicular to the field.
a. (i) Derive an expression for the magnetic field strength B required to keep a charged particle of mass m, charge q, and speed v moving in a circle of radius r in the field.
b. (ii) Using the expression obtained in part (i), calculate the magnitude of the magnetic field needed for the given alpha particles.
c. (iii) A deuteron (nucleus of deuterium, mass 3.34×10−27kg, charge +e) with the same speed enters the same magnetic field at right angles. Predict, with justification, whether its circular path will have a radius greater than, equal to, or less than 0.125m. Explain your reasoning clearly.