Calculating the capacitance of a system of two plates tilted at a small angle

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Homework Statement

A capacitor is made up of a pair of square plates, each of side length L, that are very nearly parallel (such that θ is very small) and separated by a distance D. The plates make an angle, θ, with one another. The capacitor may be thought of as being comprised of many infitesimally think strips of width, dx, and length L, which are effectively in parallel with one another. Recall that sinθ≈θ for θ<<1rad. Calculate the capacitance of the system of two plates. Capacitor.jpg attached is a picture of the problem.

Homework Equations

C=Kε₀A/d, K=1(vacum)

The Attempt at a Solution

C=Kε₀A/d=ε₀L²/d=ε₀L²∫1/(Lsinθ+D)dL (integral lower limit 0 upper limit L)
C=ε₀(LN(Lsinθ+D)-LN(0))
I believe this is right just wanted confirmation on my method...

 

[gleem]

A quick look at your answer and I see a problem ln(0) = ∞ .

 

[gleem]

You start out ok but you assumed that the charge on each elemental capacitor is constant and that is not correct.

After you solve a problem check your answer. In this case if the angle approaches 0 then the capacitance should be that of a L x L plates separated a distance D.