A spherical shell is placed in an field that otherwise would be constant E_0 = E_0 k. a) Find the field outside the sphere,

b) inside the cavity, and

c) inside the shell dielectric, in terms of the inner and outer radii, a and b, respectively, and the dielectric constant _r.

Note that in this case we have four boundary conditions (two for each surface) to find 4 different coefficients for each Legendre polynomial that are needed to describe the potential in the three different regions of the system.