Solving Spherical and Cylindrical Capacitors for Inner Radii

[meph11]

Homework Statement

I have two homework problems, both of which require me to solve the equation for the capacitance of a capacitor for the inner radius of the capacitor (one cylindrical, one spherical). This shouldn't be a problem, but I think my algebra is screwy.
a = inner radius
b = outer radius
C = capacitance
h = height of capacitor

Homework Equations

Capacitance of a Spherical Capacitor:
(i) C=4\pi\epsilon_{0}ab / (b-a)

Capacitance of a Cylindrical Capacitor:
(ii) C=2\pi\epsilon_{0}h / ln(b/a)

The Attempt at a Solution

My attempts at solving these for a are as follows:
(i) a = b*C / (C + 4*\pi*\epsilon*b)
(ii) a = b / e^{(2*\pi*\epsilon*h / C)}

 

[Delphi51]

Both are correctly derived!
What is the h in the spherical formula?

 

[meph11]

The equations are solved for a correctly?

There is no h in the spherical formula.

 

[Delphi51]

Capacitance of a Spherical Capacitor:
(ii) C=2\pi\epsilon_{0}h / ln(b/a)

(ii) a = b / e^{(2*\pi*\epsilon*h / C)}

An h is showing in each formula on my screen. Just before "/ ln(b/a)" in the first formula.

 

[meph11]

whoops, i had them labeled wrong. (i) is the capacitance of a spherical capacitor, and (ii) is the capacitance of a cylindrical capacitor. h is the height of the capacitor. Hm, I must be entering values into my calculator incorrectly... rechecking now.

 

[meph11]

Yeah, I solved the cylindrical one (ii) correctly, I just just plugging values in incorrectly.

The spherical one is still giving me issues though, I'm getting

a = b + (C / (4 * Pi * E)), which means that a will always be greater than b, an impossible situation when a is the inner radius. So I think that somewhere I've got my algebra wrong, specifically a minus sign missing somewhere.