AP Physics: Electric Potential?

[A-Man]

A capacitor is composed of two concentric spherical shells of radii a and b (b>a), respectively, that have equal and opposite charges. Just outside the surface of the inner shell, the electric field is directed radially outward and has a magnitude Eo.

a. With the use of Gauss' Law, express the charge +Q (in the region between a and b) on the inner shell as a function of Eo and a.
b. Write an expression for the electric field strength E between the shells as a function of Eo, a, and r.
c. What is the potential difference V between the shells as a function of Eo, a, and b?
d. Express the energy U stored in this capacitor as a function of Eo, a, and b.
e. Determine the value of a that should be chosen in order to maximize U, if Eo and b are fixed.

Note: I have done this problem but i am unsure of my answers. Thanks for any help you can provide.