Assume that the Faraday Cup and Grounding Cage act like coaxial conducting cylinders (ignore that there is a bottom to the Faraday Cup, and allow the height of the Grounding Cage to be equal to the height of the Faraday Cup). The inside cylinder is isolated from the outside cylinder with the outside cylinder attached to ground. Also assume that the surface charge density on the Faraday cup is uniform. Determine the following, showing all work symbolically:

a) Determine the Electric Field inside the Faraday Cup. (r < a)

b) Determine the Electric Field halfway between the Faraday Cup and the Grounding Cage.

c) Determine the Electric Field outside of the Grounding Cage. (r > b)

d) Draw the Electric Field for all of the above cases.

The solid line represents the Faraday Cup,while the dashed line represents the Grounding Cage.