Capacitance in a Sperical Shell

[Cazicami]

Homework Statement

Consider two concentric spherical metal shells of radii 2m and 4m, situated in free space and carrying uniform surface charge densities of 20nC/m² and 5nC/m² respectively.

Find the capacitance C=Q/ΔV of the spherical capacitor formed by the shells. Here Q is the total charge carrying by the smaller spherical shell and ΔV is the potential difference between points of smaller and larger shells.

We know from previous parts of the question that the electric field beyond 4m is 0 and that the electric field for 2 < r < 4 is equivalent to 9x10^-3x1/r² because of the enclosing the inner shell.

Homework Equations

C=Q/ΔV
ΔV = -∫$∫^{a}_{b}$ E . dl

The Attempt at a Solution

My attempt was simply to use the given equations to calculate C, however my answer and the solution in the past paper are not the same, and I don't understand why not. I am considering that the solutions may be wrong, but I don't think my physics is good enough to be better than my lecturers.

I've attached my solutions in a photo, as well as the lecturers.

 

[TSny]

I believe your answer is correct. The typed solution appears to be correct up until values were substituted for a and b. ab/(a-b) evaluates to 4, whereas they appear to get 2.

 

[rude man]

The differing charge numbers and potential difference are of course a smokescreen.

Your solution is correct.

 

[Cazicami]

Thanks very much guys :)