# Formula: 1. Maxwell Equation in Integral Form Electric field (E field)    Electric charge

## Electric field

Unit
This quantity is a vector field (it assigns a field vector to each point in space) and tells how large the electric force on a test charge would be if it were placed in a particular location.

## Surface

The (imaginary) surface over which the electric field $$\class{blue}{\boldsymbol{E}}$$ is integrated. This can be, for example, a spherical surface or a cylindrical surface. For example, to calculate the $$\class{blue}{\boldsymbol{E}}$$ field inside a charged sphere, this imaginary surface is placed inside the charged sphere.

Here $$\text{d}\boldsymbol{a}$$ is a infinitesimal piece of the surface. By definition the direction of $$\text{d}\boldsymbol{a}$$ is perpendicular on the surface.

## Electric charge

Unit
This is the charge that is enclosed by the selected surface $$A$$.

## 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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