Conducting sphere of radius a and a thin spherical shell (radius b = 2.5a) are arranged concentrically, as shown in the figure. The outer shell is grounded (V = 0) and the net charge in the inner sphere is Q. For each part, find the result in terms of a, Q, and other physical constants. Also, provide a written explanation in words of how you arrived at each answer.
A. The surface charge density on the spherical shell.
B. The electric field in the region 0 < r < a.
C. The electric field in the region a < r < b.
D. The potential difference between the outer shell and the inner sphere.
E. The potential difference between the surface of the inner sphere and its center (r = 0).