Alexander Fufaev

Formula: 1. Maxwell Equation in Integral Form

Electric flux and enclosed charge (1st Maxwell equation)

Electric field

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.


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

This is the charge that is enclosed by the selected surface \( A \).

Vacuum Permittivity

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