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

## 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 seperated 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...

#### Attachments

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

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