# Capacitance capacitor parallel plate with dielectric (Gauss)

• Ark236
In summary, the conversation discusses a doubt with calculating the capacitance of a capacitor with parallel plates and a dielectric in the middle. The conversation includes equations such as ∫D⋅ds=Q, D=E+γP, and C=Q/V, and also considers the electric field and polarization of the plates. The conversation concludes with a question about the error in the calculations and the assumption that D is zero outside the capacitor.
Ark236

## Homework Statement

I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle.

https://ibb.co/b0W4BQ

∫D⋅ds=Q
D=E+γP
C=Q/V

## The Attempt at a Solution

Suppose the top plate has a positive charge and the bottom plate has a negative charge.

To calculate vector displacement in the upper plate, we occupy the gauss law, use a Gaussian box. On the outside of the top plate the polarization P is 0 and there is an electric field E. At the bottom of the plate there is an electric field E and a polarization P due to the dielectric.
If we consider only the top plate:

∫D⋅ds=[D][/out]A+[D][/down]A=Q

[D][/out]=E
[D][/down]=E+γP

If we consider the complete system (both plates)

∫D⋅ds=2*[D][/out]A+2*[D][/down]A=Q

[D][/out]=E
[D][/down]=E+γP

The field inside is 2 E.

What is the error, I do not understand. D is zero outside from capacitor?
Thank you

Last edited:
At a first glance I see some equation problems since D is not equal to E D=epsilonxE. On the other side the elctric field outside the plates is considered to be 0 since the infinite parallel plates asumption is used when Gauss Law is applied. You should check your relevant equations

## 1. What is capacitance?

Capacitance is the ability of a system to store electrical charge. It is measured in Farads (F) and is represented by the symbol C.

## 2. How does a capacitor work?

A capacitor consists of two conductive plates separated by a dielectric material. When a voltage is applied across the plates, an electric field is created, causing one plate to accumulate positive charge and the other to accumulate negative charge. This separation of charge creates a potential difference between the plates, allowing the capacitor to store electrical energy.

## 3. What is a parallel plate capacitor?

A parallel plate capacitor is a type of capacitor where the two conductive plates are parallel to each other. This type of capacitor is commonly used because it has a simple and predictable structure, making it easy to calculate its capacitance.

## 4. How does the dielectric material affect the capacitance of a parallel plate capacitor?

The dielectric material placed between the plates of a parallel plate capacitor affects the capacitance by reducing the strength of the electric field between the plates. This reduces the potential difference and increases the capacitance, as the amount of charge that can be stored on the plates increases.

## 5. What is Gauss's law and how is it related to capacitance?

Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. In the case of a parallel plate capacitor, Gauss's law can be used to calculate the electric field strength between the plates, which is necessary for determining the capacitance of the capacitor.

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