Determine the magnitude of the charge on the inner and outter surface of sphere

[gothloli]

Homework Statement

A hollow conducting spherical shell has an inner radius of 8 cm and an outer radius of
10 cm. The electric field at the inner surface of the shell, Ei, has a magnitude of 90 N/C
and points toward the centre of the sphere, and the electric field at the outer surface, Eo,
has a magnitude of 80 N/C and points away from the center of the sphere (see Figure A).
Determine the magnitude of the charge on the inner surface and the outer surface of the
spherical shell.

Homework Equations

For the inner surface: E =kq_t/r1r^{3}
For the outer surface E = kq_t/r₂^{2}

The Attempt at a Solution

This uses Gauss's law. For the inner surface, set gaussian surface, with r1<r, r is the inner radius.
For outer surface, gaussian surface outside the sphere. r2>rs which is radius of shell.
I'm stupid I don't know what to do.

 

[haruspex]

For there to be a field inside the conducting shell, there must be some isolated charge inside it. By symmetry, you can consider that to be at the centre. Let that charge be q_c. There are also charges spread over the inside surface of the sphere, q_i say, and on the outside surface, q_o.
Can you write down an expression for the potential at distance r from the centre? To start with, just consider a single shell of charge at some radius a. You need to consider r < a and r > a separately. When you've got that, you can write down the total potential from the three charges just by adding them up.