\Section[
    \eng{Electromagnetism}
    \ger{Elektromagnetismus}
]{em}
    \begin{formula}{speed_of_light}
        \desc{Speed of light}{in the vacuum}{}
        \desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
        \constant{c}{exp}{
            \val{299792458}{\m\per\s}
        }
    \end{formula}
    \begin{formula}{vacuum_relations}
        \desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{speed_of_light}}
        \desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{}
        \eq{
            \epsilon_0 \mu_0 = \frac{1}{c^2}
        }
    \end{formula}

    \begin{formula}{poisson_equation}
        \desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\Phi$ Potential}
        \desc[german]{Poisson Gleichung in der Elektrostatik}{}{}
        \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}}
        \TODO{double check $\Phi$}
    \end{formula}

    \begin{formula}{poynting}
        \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{}
        \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes  [$\si{\W\per\m^2}$]}{}
        \eq{\vec{S} = \vec{E} \times \vec{H}}
    \end{formula}

    \begin{formula}{electric_field}
        \desc{Electric field}{}{\QtyRef{electric_field}, \QtyRef{electric_scalar_potential}, \QtyRef{magnetic_vector_potential}}
        \desc[german]{Elektrisches Feld}{}{}
        \eq{\vec{\E} = -\Grad\Epotential - \pdv{\vec{A}}{t}}
    \end{formula}

    \begin{formula}{hamiltonian}
        \desc{Hamiltonian of a particle in an electromagnetic field}{In the \fqEqRef{ed:em:gauge:coulomb}}{\QtyRef{mass}, $\hat{p}$ \fqEqRef{qm:se:momentum_operator}, \QtyRef{charge}, \QtyRef{magnetic_vector_potential}, \ConstRef{speed_of_light}}
        \desc[german]{Hamiltonian eines Teilchens im elektromagnetischen Feld}{In der \fqEqRef{ed:em:gauge:coulomb}}{}
        \eq{
            \hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2
        }
    \end{formula}


    \Subsection[
        \eng{Maxwell-Equations}
        \ger{Maxwell-Gleichungen}
    ]{Maxwell}
        \begin{formula}{vacuum}
            \desc{Vacuum}{microscopic formulation}{}
            \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
            \eq{
                \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
                \Div \vec{B} &= 0 \\
                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
                \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t}
            }
        \end{formula}

        \begin{formula}{material}
            \desc{Matter}{Macroscopic formulation}{}
            \desc[german]{Materie}{Makroskopische Formulierung}{}
            \eq{
                \Div \vec{D} &= \rho_\text{el} \\
                \Div \vec{B} &= 0 \\
                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
                \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
            }
        \end{formula}


        \Subsubsection[
            \eng{Gauges}
            \ger{Eichungen}
        ]{gauge}
            \begin{formula}{coulomb}
                \desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
                \desc[german]{Coulomb-Eichung}{}{}
                \eq{
                    \Div \vec{A}  = 0
                }
            \end{formula}


        \TODO{Polarization}

    \Subsection[
        \eng{Induction}
        \ger{Induktion}
    ]{induction}
        \begin{formula}{farady_law}
            \desc{Faraday's law of induction}{}{}
            \desc[german]{Faradaysche Induktionsgesetz}{}{}
            \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
        \end{formula}

        \begin{formula}{lenz}
            \desc{Lenz's law}{}{}
            \desc[german]{Lenzsche Regel}{}{}
            \ttxt{
                \eng{
                    Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
                }
                \ger{
                    Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
                }
            }
        \end{formula}
