1 Answer
The relationship between **electric flux density** (**D**) and **volume charge density** (**ρ<sub>v</sub>**) is given by **Gauss's Law** in **differential form**.
### Gauss's Law (Differential Form):
\[
\nabla \cdot \mathbf{D} = \rho_v
\]
### What this means in simple words:
- **Electric flux density (D)** tells us how much electric flux is flowing **through a unit area**. Its unit is **Coulombs per square meter (C/m²)**.
- **Volume charge density (ρ<sub>v</sub>)** tells us how much electric charge is **present in a unit volume**. Its unit is **Coulombs per cubic meter (C/m³)**.
The equation says:
> The divergence of electric flux density (**∇·D**) at any point in space is equal to the volume charge density (**ρ<sub>v</sub>**) at that point.
---
### In integral form:
If you want to see it in a more physical form, Gauss's Law also says:
\[
\oint_{S} \mathbf{D} \cdot d\mathbf{A} = \int_{V} \rho_v \, dV
\]
- The **left side** shows the total electric flux **coming out of a closed surface**.
- The **right side** shows the **total charge inside that volume**.
---
### Summary:
- **Electric flux density (D)** is linked to **charge density (ρ<sub>v</sub>)** through Gauss’s law.
- Where there is more charge in a region, the **flux density D is stronger**.
- This helps in understanding electric fields in materials and space.
Would you like a simple example or diagram to visualize it better?
### Gauss's Law (Differential Form):
\[
\nabla \cdot \mathbf{D} = \rho_v
\]
### What this means in simple words:
- **Electric flux density (D)** tells us how much electric flux is flowing **through a unit area**. Its unit is **Coulombs per square meter (C/m²)**.
- **Volume charge density (ρ<sub>v</sub>)** tells us how much electric charge is **present in a unit volume**. Its unit is **Coulombs per cubic meter (C/m³)**.
The equation says:
> The divergence of electric flux density (**∇·D**) at any point in space is equal to the volume charge density (**ρ<sub>v</sub>**) at that point.
---
### In integral form:
If you want to see it in a more physical form, Gauss's Law also says:
\[
\oint_{S} \mathbf{D} \cdot d\mathbf{A} = \int_{V} \rho_v \, dV
\]
- The **left side** shows the total electric flux **coming out of a closed surface**.
- The **right side** shows the **total charge inside that volume**.
---
### Summary:
- **Electric flux density (D)** is linked to **charge density (ρ<sub>v</sub>)** through Gauss’s law.
- Where there is more charge in a region, the **flux density D is stronger**.
- This helps in understanding electric fields in materials and space.
Would you like a simple example or diagram to visualize it better?