# When does the surface charge density equal the electric flux density?

• FOIWATER
In summary, surface charge density is a measure of the distribution of electric charge on a surface, while electric flux density is a measure of the electric flux per unit area of a surface. To calculate surface charge density, the total charge on the surface is divided by the total area. When the surface is a perfect conductor, surface charge density and electric flux density are equal. The relationship between surface charge density and electric flux density is given by D = εE, where D is the electric flux density, E is the electric field, and ε is the permittivity of the medium. This relationship shows that the electric flux density is directly proportional to the electric field and inversely proportional to the permittivity of the medium.
FOIWATER
Gold Member

## Homework Statement

The electric field intensity in polystyrene (relative permittivity 2.55) filling the space between the plates of a parallel plate capacitor is 10kV/m. The distance between the plates is 1.5mm.
Calculate the surface charge density of free charge on the plates,
and the surface density of polarization charge

rho s = D dot an

## The Attempt at a Solution

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I am having a hard time seeing how the surface charge density equals the d field normal to the surface in this case?

Is it because it's at a conducting surface

## 1. What is surface charge density?

Surface charge density is a measure of the distribution of electric charge on a surface. It is defined as the amount of electric charge per unit area of the surface.

## 2. What is electric flux density?

Electric flux density, also known as electric displacement, is a measure of the electric flux per unit area of a surface. It is defined as the electric flux per unit area perpendicular to the direction of the electric field.

## 3. How do you calculate surface charge density?

To calculate surface charge density, you divide the total charge on the surface by the total area of the surface. The formula for surface charge density is Q/A, where Q is the total charge and A is the total area.

## 4. When does surface charge density equal electric flux density?

Surface charge density and electric flux density are equal when the surface is a perfect conductor. In this case, the electric flux will be normal to the surface and the surface charge density will be equal to the electric flux density.

## 5. What is the relationship between surface charge density and electric flux density?

The relationship between surface charge density and electric flux density is given by the equation D = εE, where D is the electric flux density, E is the electric field, and ε is the permittivity of the medium. This relationship shows that the electric flux density is directly proportional to the electric field and inversely proportional to the permittivity of the medium.

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