Conducting surface inside conducting surface

Question

Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday cage. There's no charge or electric field inside and and the charges on the exterior distribute themselves so as to cancel the E field.

My questions is this: let's say this first surface, is now enclosed completely within a second bigger surface, with the same properties, and they don't touch anywhere. Then the same thing would happen to the second Faraday cage, and so the E field inside would cancel. But if the E field inside cancels, then the charges on the first, now interior, Faraday cage redistribute themselves to their original positions, since they no longer need to compensate for any E field.

Is this right? And is it generally true that when multiple closed conducting surfaces enclose each other, the only one that acts as a Faraday cage is outermost one?

Edit: I'm sorry for being ambiguous. The original assumption also has a constant, non-varying electric field, exterior to both spheres. The charges on the first one, without the second one, will arrange themselves as to cancel the E field inside the sphere. Then this first sphere, with its exterior charges affected by the external field, is enclosed within the second one. My question is what happens now? Intuition says the second sphere will cancel the E field inside, this including the first sphere, so, locally to the 1st sphere, the external E field is removed, so the charges arrange themselves to their original positions.

Answer 1

I'm a little confused about what system you're asking about. The charges will only be nonuniform if there is an external electric field. In your first paragraph you acknowledge that the internal field is zero partly because there is no charge within a sample volume in the sphere's interior. If there's an additional charged sphere in that interior the statement obviously no longer holds. So let me speak of this system:

• two concentric spheres as you've described
• an electric field, external to both, constant in some arbitrary direction
• the internal sphere has a charge on it (the external sphere may or may not have a charge, I don't care)

The law establishing that the interior of a sphere will have no field still applies to the internal sphere and does not apply to the external one. The external sphere will still be constant potential. The field outside that sphere will be quite non-symmetric due to the summation of potentials from the external field and the spheres, however, the field within the larger sphere will still be radially symmetric.