Electric field between electrodes of half-filled spherical capacitor

[sodaboy7]

Homework Statement

Half the space between two concentric electrodes of a spherical capacitor is filled with uniform isotropic dielectric with permittivity ε. The charge of the capacitor is q. Find the magnitude of electric field strength between the electrodes as a function of distance r from center of electrode.

Answer → E = q/2∏ε_o(ε + 1)r²

Homework Equations

V₁ - V² = -∫E.ds

The Attempt at a Solution

I tried to find the potential diference between electrod using above equation but its not working

 

[Simon Bridge]

Consider - what is the field between the plates without the dielectric?
How does that change when the space is totally filled with dielectric?
Lynchpin: the situation is two capacitors in series.

But if you have been explicitly told to derive this with gausses law:
http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter27/chapter27.html#Heading10