Solve Dielectric Problem: Parallel Plate Capacitor w/ Wedge Insert

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Homework Statement

A parallel plate capacitor has a capacitance C when there is no dielectric inside of it. Suppose a wedge
of material with dielectric constant K is inserted in between the plates of the capacitor (see figure). The
bottom face of the wedge has the same area as the plate of the capacitor. The height of the wedge is
equal to the thickness of the capacitor, t on the left edge and varies linearly until the height is zero on
the right edge. What is the new capacitance with this dielectric inserted?
HINT: See if you can split up the capacitor into small capacitors that each have a dielectric in them that
you know how to deal with.

Homework Equations

C = KC0

C = εA/d

The Attempt at a Solution

Well, I first started with slicing the capacitor vertically into n small slices and from here to set up an integral, but I'm not sure how to set up the integral...

 

[UltrafastPED]

The "mini capacitors" all share the same bus, so they are parallel ... so to get the total capacitance you just add them up.

For each little bit, the amount of dielectric present is proportional to the distance from the edge, so you just need to express this relationship.