One component of a device for producing a beam of spin polarized protons for use in nuclear research is a spherical deflector. The ion source may be described in class. The deflector is composed of two sections of spheres that face each other as capacitor plates. Each section forms a quarter arc and as negatively charged Hydrogen ions pass through this region their path is deflected in a circular arc by 90°. Hydrogen enters this region at a speed vo = 3.1×106 m/s. The path of the Hydrogen between the plates is a circle of radius 30 cm. The inner plate is cut from a sphere of radius 28 cm, while the outer plate is cut from a sphere of radius 32 cm. Assume no fringing effect at the edges and determine the potential difference needed between the plates to accomplish this design goal. Hint: Make the hydrogen orbit between two charged spheres of these dimensions.
As with any challenge problem your solution must be complete and presented in an orderly manner, including any figures, coordinate systems, etc.