# Formula: 1. Maxwell Equation in Differential Form Electric field    Charge density

## Electric field

Unit
Electric field indicates how large and in what direction the electric force on a charge would be if that charge were placed at location $$(x,y,z)$$.

The divergence field is the scalar product between the Nabla operator $$\nabla$$ and the electric field $$\class{blue}{\boldsymbol{E}}$$: $\nabla ~\cdot~ \class{blue}{\boldsymbol{E}} ~=~ \begin{bmatrix} \frac{\partial}{\partial x} \\ \frac{\partial}{\partial y} \\ \frac{\partial}{\partial z} \end{bmatrix} ~\cdot~ \begin{bmatrix} \class{blue}{E_{\text x}} \\ \class{blue}{E_{\text y}} \\ \class{blue}{E_{\text z}} \end{bmatrix}$

The divergence field is no longer a vector field but a scalar function. The divergence field $$\nabla ~\cdot~ \class{blue}{\boldsymbol{E}}(x,y,z)$$ at the location $$(x,y,z)$$ can be positive, negative or zero. With positive divergence, there is a positive electric charge (a source) at the location $$(x,y,z)$$. When the divergence is negative, there is a negative electric charge (a sink) at the $$(x,y,z)$$ location. If, on the other hand, the divergence at the location $$(x,y,z)$$ is zero, then there is no electric charge there.

## Charge density

Unit
Space charge density indicates how many electric charges per volume there are in a space region.

## Vacuum Permittivity

Unit
The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value: $$\varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}}$$

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