E field profile in a capacitor with two different dielectric material

[enroger0]

Hi everyone, this is not a homework, I'm actually dealing with the case in real life here. If this turns out to be standard textbook stuff then I'm sorry as I haven't studied this before.

Suppose a plate capacitor has two different dielectric material layer sandwiched in it. Then a fixed voltage is applied on it.

The simplest consideration would be that E field is constant everywhere despite the different dielectric constant of the two layers, this was my first thought. But it didn't feel right as I consider the energy, since system tends to minimize energy against fixed boundary condition.

So with the same E-field strength, the material will store more energy with a higher dielectric constant. Minimizing the energy will yield that the higher dielectric constant material will have a smaller voltage drop across it, is this result right?

 

[Bob S]

The easiest way to think about this is to imagine two real capacitors with same plate areas, connected in series, one with the one dielectric and its thickness, and the second dielectric and its thickness. Now apply voltage to the two caps in series, and calculate the voltage across each cap.

 

[enroger0]

Ha! Dumb me... Then it is true that voltage drop faster in smaller dielectric material. Thanks