Question on charged spheres and shells

[Markv]

Homework Statement

Suppose we are given a metallic sphere with charge Q1 and electric potential V1 and radius a. Then it is surrounded by a metallic spherical shell with charge Q2 and electric potential V2 with inner and outter radius b and c.

What is the charge and the electric potential everywhere??

Homework Equations

dV = E*dr

V=K*Q/r

The Attempt at a Solution

First all the charge has to be in the surfaces because they are all conductors.

To calculate the charge on the sphere I would integrate the electric field from a to b, then from b to c (where it is 0) and finally from c to infinite.

Now that I have Q1, I know that the charge in the inner surface of the shell must the -Q1 because the total charge inside a conductor must be cero.

Now comes the part where I am stuck.

To calculate the charge on the outter surface of the shell should I just use the formula por the electric portential:

V2=k^*Q2/c

And that's the charge on the outter surface, or instead that's the total charge of the shell and I should do something like this:

Q inner surface + Q outter surface = Total Q

And isolate the outter surface charge from there.

Thank you.

 

[sigmaro]

Actually, i couldn't quite understand why did question give all q v and d, if you know two (in this case) you can get other one.
Anyway, that is easy, don't confuse yourself with integrals.
lets start from outermost place. there we only deal with the charge density at radius=c. by perfect symmetry and gauss' law, we don't touch other things and potantial there is simply kq'/c=V2
no probs with that right?
now as we go in this shell, there is no potantial change till (including) r=b. and there as you mentioned there is a charge distribution of q''=Q1
then, as we go in by gauss' law we only deal with Q1 and potantial difference between b and a is simply Va-Vb=kQ1/a - kQ1/b and we know Vb=Vc=kQ2/c
rest is ok i think, if you have further problems feel free to ask