Three concentric shells, one uncharged (Potential)

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

See figure attached for my attempt.

I'm confused as to how I am supposed to use these 3 electric fields, E1, E2 and E3, as well as the potential of the middle shell, V = 1kV (with reference point at infinity), to calculate the charge on the middle shell, $$q_{mid}$$

I know I should be doing some integration over the electric fields in order to get the potential, but it's not obvious to me what path I should take to only have the potential of the middle shell.

The solution gives it as from c to d, and then from e to infinity.

Why so?

Can someone clarify? Is the picture I drew incorrect?

Thanks again!

 

[rude man]

You wrote an expression for the field inside the middle shell which you know can't be right, since the E field inside a conductor is zero.

But you have the right idea in using Gauss' theorem. Use it for the spaces between the shells, and integrate the E fields accordingly to get the potentials. Call the charge on the middle shell Qb for the moment.

Then, you need to compute Qb given the middle shell's potential as 1 kV. Careful how you do this, it isn't just kQb/Rbo where k = 9e9 and Rbo is the outer radius of the middle shell (why not?).