There is a section of a conducting rod of radius R1 and length L inside a thin-walled coaxial conducting cylindrical shell of radius R2=10R1. The net charge on the rod is Q1, while the net charge of the shell is Q2= -3Q1.

a) Using Gauss' Law, find the electric field (magnitude and direction) between the cylindrical shell and the rod. The electric field will depend on the distance r from the central axis of the solid rod. Put your answer in terms of R1, L, Q1, r, and physical constants. Assume that the rod and cylindrical shell are very long (L>>R2) and focus on the region away from the end caps of the solid rod.

i) Identify the Gaussian surface to use and draw a diagram

ii) Find the electric flux through the Gaussian surface. (L>>R2)

iii) Find the amount of charge enclosed by the surface.

iv) Solve for the electric field

b) Using Gauss' Law, find the electric field (magnitude and direction) outside the cylindrical shell (r>R2). Put your answer in terms of R1, L, Q1, r, and physical constants.

c) Find the net charge on the inner and outer edge of the cylindrical shell. Put your answer in terms of Q1.