An insulated uniformly charged sphere of radius R, has been smeared with charge q uniformly throughout its volume. Now this sphere is surrounded with a charged conducting spherical shell of inner radii a and outer radii b, smeared with charge −2q.
What is the resulting →E for all the regions?
So the case where the conducting shell is uncharged, the inner surface will be induced with charge −q and the outer surface with charge, +q; and one can easily find the →E using Gauss' Law.
Now in the case of a charged spherical shell, the charge will be so distributed so that inside the conductor the electric field is zero.
Now naively if I apply Gauss's Law, then I come to the conclusion that on the inner surface with radii a, the induced charge is −q, so as to cancel the field in side the conductor and then on the outside surface the induced charge is again, −q, so as the total charge on the conducting sphere is −2q.
But as we know that if their is a charged cavity inside the conductor, it shields the cavity from external charged sources. So outside the conductor we should have seen a charge +q. So where is my logic failing?
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