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## Homework Statement

Find the capacitance of the capacitor shown in the figure. Asume H << L.

http://imageshack.us/a/img39/1935/capacitor.png [Broken]

## Homework Equations

Capacitance of a plate parallel capacitor with a dielectric material e: eA/H where A denotes the area of the plate, and H the separation between plates

## The Attempt at a Solution

My thoughts:

The line separating the dielectric materials can be written as f(x)=Hx/L

**(I rotated the system so the line starts in the origin)**

The system can be considered as multiple parallel capacitors in which the proportion of the dielectric changes at the rate given by the linear equation.

First, I calculated the differential capacitance of two capacitors in series, whose lenght is dx. Their capacitances are given by:

[tex]C1= \frac{e1Ldx}{H-\frac{Hx}{L}}[/tex]

[tex]C2= \frac{e2Ldx}{\frac{Hx}{L}}[/tex]

After getting the equivalent capacitance, I integrated from 0 to L, hoping to get the total capacitance of the system.

Thing is, when I assume e1=e2, I don't get the capacitance of a normal plate parallel capacitor with one dielectric material.

I really want to know if the logic of my process is okay, because I've tried about 5 times to check if calculus are done right.

Sorry for my english and the simplicity of my explanation, I'll try to explain further when I get a little more time.

Thanks in advance!

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