Im having trouble understanding the electric field within a sphere of charge. Here's the problem. Suppose we have a hollow conduction sphere of negative charge, say its inner radius is 5cm. Inside this hollow sphere we have another solid charged spherical conductor whose radius is 2cm. Now i want to find the electric field 3cm away from the solid inner conducting sphere (the r=2cm sphere). Also lets say the charge is opposite in sign to the outer shell.
My understanding, which seems to be incorrect is that the inner solid sphere polarizes the outer one, thus there is also an electric field due to the shells inner surface where there is negative charge residing. Why is this assumption incorrect and why is there only an electric field due to the solid inner sphere at this distance.