Two concentric conducting spherical shells of radii Ri and R0 respectively, where R0> Ri. The outer shell has a net charge Q and the inner shell with -Q. The space between the shells has a linear dielectric of relative permittivity er = e0 + kr where r represents the distance to the geometric center of the system. In terms of the quantities delivered:

1. Make a scheme of the system specifying each of the elements mentioned in the problem statement
2. Calculate the densities of free charge and bound charge in the system. Point out on your diagram where these bound charges are located, and explain why.
3. Calculate the electrical displacement
4. Calculate the electric field
5. Calculate the capacitance
6. Calculate the configuration energy.

An insulating cylinder of radius R and length L (where L>> R, very long cylinder), has a uniformly distributed charge density Y. However, at a distance "a" from the long axis of symmetry of the cylinder is the geometric center of an empty cavity of spherical geometry of radius "b", where a + b 

1. Draw a schematic of the system described above denoting each of the characteristics mentioned above.
2. Calculate the electric field E in all space.
3. Calculate the potential V in all space.
4. Calculate the density of charge induced on the surfaces of the conducting sphere.