Ohms law for concentric spherical shells

[zezima1]

Look at the attached problem with solutions. I don't understand what the author means in c) when he says that succesive shells contribute less and less because the cross sectional area grows proportional to r². The flux through a closed surface is always the same (Gauss' law). Rather the reason why the b becomes negligible is in my opionion that you are very far away from the shell. Can anyone explain what the author means by this "succesive shells contribute less and less"?

 

[TSny]

There is an elementary formula for the resistance, dR, of a thin slab of material of thickness dx and cross-sectional area A: dR = $\frac{dx}{σA}$.

See if you can apply this to a thin spherical shell of radius r and thickness dx = dr.

How does the resistance of the shell depend on r? What happens as r goes to ∞?

If you integrate the expression for dR from r = a to r = b you should get the formula for the total resistance of the material that lies between the sphere of radius r = a and the sphere of radius r = b.