A charged particle is injected, with a velocity $,$ into a region with a constant magnetic field, $.$

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a$.$ Show that the particle will undergo circular motion, and write an expression for the radius of the circular motion in terms of the mass, charge, and velocity of the particle and the strength of the magnetic field. $(10$ points$)$

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b$.$ Say that the particle is singly ionized $($missing only one electron with charge $),$ and that its velocity was $$as it was injected into a magnetic field of strength $.$ What is the difference in the radii of the circular motion for Uranium $$which has an atomic mass of about $235$ u$,$ and $$which has an atomic mass of about $238$ u$,$

where $.(10$ points$)$

This difference in radii is easily detected and the device is known as a mass spectrometer.

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