What Happens to Surface Charges When a Grounded Wire Connects to a Metal Shell?

[Pietjuh]

Suppose you've got a metal sphere of radius R and it is surrounded by a metal spherical shell with inner radius $$r_a$$ and outer radius $$r_b$$. The metal sphere has total charge Q. The first thing i had to calculate was what the induced surface charges are on the shell. That was pretty easy, but they then posed the following question.

Suppose you'd connect a wire to the spherical shell that is connected to the earth. What happens to the surface charges of this shell.

I thought because of the grounding wire, all the free charges float to the earth, leaving the shell positively charged. But you've also got the attraction of the sphere at the center. So basically i don't have a clue what happens

Can anybody give some hints?

 

[StatusX]

Connecting a conductor to groud gives it a zero voltage. In other words, it would take no work to move a charge from very far away to the surface of the outer conductor after connecting the wire. What does this say about the field outside the conductor and the total charge on both?

 

[Pietjuh]

Since E is the gradient of the potential, it would mean the total electric field is zero. Then according to gauss's law the total charge would be zero also. So this would mean the electric field of the sphere doesn't create a induced charge on the shell and is also non-zero in the region between the sphere and the shell. Right?

 

[StatusX]

No, because then there would be a field outside the sphere/shell assembly. There has to be zero total charge on all conductors.