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In the existence of an electric field, the free electrons start drifting ,thus creating an opposition field, which keeps growing as more electrons start drifting. When this opposition field becomes equal to the original field, electrons stop drifting, and we have achieved steady state, and there is no electric field inside the conductor. Will this happen always? Consider a point charge placed at the center of a metallic shell. We can draw a Gaussian surface enclosing the charge, and thus, the field inside cannot be zero.

1.Why did the mechanism i mentioned earlier not work here?

2.When exactly then, can we say that there exists no field inside the conductor? Or is it that no field exists in the inside of the conductor due to external charges?.

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  • $\begingroup$ What do you mean by a metallic "shell"? Is the region where the charge is placed filled with conductive material or insulator? If it's filled with conductive material, what did you do with all the other charges that are normally present in a conductor? $\endgroup$ – The Photon Jan 26 '20 at 4:36
  • $\begingroup$ I meant a hollow ,conducting sphere with a point charge on its center. $\endgroup$ – satan 29 Jan 26 '20 at 4:43
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    $\begingroup$ So what's the conflict? The rule is there can't be a static electric field within a conductive material. No rule against fields in insulating material. (This is basically a capacitor with your charge at the center as one "plate" and the surrounding shell as the second "plate") $\endgroup$ – The Photon Jan 26 '20 at 4:45
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Consider a point charge placed at the center of a metallic shell. We can draw a Gaussian surface enclosing the charge, and thus, the field inside cannot be zero.

If you are saying you'd make the Gaussian surface between the outer and inner surfaces of the conductive shell, you're neglecting the separation of charge in the conductor.

When you place the fixed charge (let's call it "$q$") in the center of the shell, it will attract an opposite charge $-q$ to the inner surface of the conductive shell, and push other charge with value $q$ to the outer surface of the shell. (i.e. some of the charge present in the conductor is separated, with charge of the opposite sign as the center charge moving to the inner surface of the shell, and charge of the same sign as the center charge moving to the outer surface of the shell)

So a Gaussian surface in the hollow area within the shell will surround charge $q$, as we expect, and there is a field between the center charge and the inner surface of the shell.

A Gaussian surface between the surfaces of the shell will surround a net charge of $q-q=0$, and, as we expect, Gauss' Law predicts 0 field in the conductive material.

And a Gaussian surface outside the shell surrounds a net charge of $q-q+q = q$, so again there will be an electric field in the insulating material surrounding the shell.

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