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Ohms law for concentric spherical shells

  1. Jun 12, 2012 #1
    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"?
     

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  3. Jun 12, 2012 #2

    TSny

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

    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.
     
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