Homework Help: Electrostatics problem

Suppose you've got a metal sphere of radius R and it is surrounded by a metal spherical shell with inner radius [tex]r_a[/tex] and outer radius [tex]r_b[/tex]. 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 :rofl:

Can anybody give some hints?

 

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 doesnt create a induced charge on the shell and is also non-zero in the region between the sphere and the shell. Right?