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a)Find the field for every point between the spheres.

b)Compute the charge distribution for the inner sphere.

c)Compute the surface density charge for the dielectric at r=a.

Well, I don't know how to start with this. It bothers me that the dielectric fills just one half of the space between the spheres, specially bothers me the interface between the dielectric and the "empty" space (the space is actually filled by the electric field), the problem is I don't know how to considere the induced charge on that interface, and I don't how ti find the entire electric field.

I was tempted to write that in the space within the dielectric the field is just:

[tex]E=\frac{Q}{4\pi \epsilon r^2}[/tex]

And the "empty" space has a field:

[tex]E=\frac{Q}{4\pi \epsilon_0 r^2}[/tex]

But then I wouldn't be having in mind the polarization on the dielectric.