Force between proton in a conducting shell and electron outside of shell? There's a proton inside a conducting shell and an electron outside of it. Inside the shell, there is no field due to the electron, but the electron feels the field due to the proton. Therefore the electron should move towards the immobile proton, but what happened to Newton's third law? Does the whole shell move? 
 A: The whole shell moves because the electric field experienced by the outer electron has its origin in positive charges induced by the inner proton on the outer metal surface equivalent to the proton charge. The metal shell would even move without a proton inside because the electron induces positive charges on the surface near the electron so that a net attraction occurs. All this, of course, are minimal effects when the whole setup is floating in free space. And, as M. Enns has alluded to above, there is, of course, a field due to the proton inside the shell which induces negative charges on the inner surface that exert a force on the proton.
A: The error that you have made is to apply Newton's third law incorrectly.  
On the conducting sphere there are two sets of induced charge.
One set of positive and negative induced charges is due the field of the electron having to be negated so that there is no electric field inside the conducting sphere.
These positive and negative induced charges reside on the outside of the conducting sphere.
So you are correct in your assertion that the proton does not feel the effect of the electron directly.
Put another way - the proton does not know that there is an electron outside the conducting shell.
The other set of induced charges are produced by the proton and they are present to ensure that the electric field inside the conductor is zero.
These charges reside on both the inside (negative) and the outside (positive) of the conducting sphere.  
So on the outside of the conducting sphere you have induced charges produced by the presence of the electron and the proton.  
There is a force on the electron due to the induced charges on the outside of the conducting sphere  
and the Newton's third law pair to this force is that 
there is force on the induced charges on the outside of the conducting sphere due to the electron.
So indirectly, via the induced charges on the outside of the conducting sphere produced by the proton, the electron feels the presence of the proton.  
Inside the sphere 
there is a force on the proton due to the induced negative charges that it has induced on the inside of the sphere
and the Newton's third law pair to this force is that 
there is a force on the induced negative charges on the inside of the sphere due to the presence of the proton.
