110 lines
4.4 KiB
TeX
110 lines
4.4 KiB
TeX
\Section{em}
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\desc{Electromagnetism}{}{}
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\desc[german]{Elektromagnetismus}{}{}
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\begin{formula}{vacuum_speed_of_light}
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\desc{Speed of light}{in the vacuum}{}
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\desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
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\constant{c}{exp}{
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\val{299792458}{\m\per\s}
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}
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\end{formula}
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\begin{formula}{vacuum_relations}
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\desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{vacuum_speed_of_light}}
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\desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{}
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\eq{
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\epsilon_0 \mu_0 = \frac{1}{c^2}
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}
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\end{formula}
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\begin{formula}{poisson_equation}
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\desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\Phi$ Potential}
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\desc[german]{Poisson Gleichung in der Elektrostatik}{}{}
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\eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}}
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\TODO{double check $\Phi$}
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\end{formula}
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\begin{formula}{poynting}
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\desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field}{}
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\desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes [$\si{\W\per\m^2}$]}{}
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\quantity{\vecS}{\W\per\m^2}{v}
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\eq{\vec{S} = \vec{E} \times \vec{H}}
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\end{formula}
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\begin{formula}{electric_field}
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\desc{Electric field}{}{\QtyRef{electric_field}, \QtyRef{electric_scalar_potential}, \QtyRef{magnetic_vector_potential}}
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\desc[german]{Elektrisches Feld}{}{}
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\eq{\vec{\E} = -\Grad\Epotential - \pdv{\vec{A}}{t}}
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\end{formula}
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\begin{formula}{hamiltonian}
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\desc{Hamiltonian of a particle in an electromagnetic field}{In the \fRef{ed:em:maxwell:gauge:coulomb}}{\QtyRef{mass}, $\hat{p}$ \fRef{qm:se:momentum_operator}, \QtyRef{charge}, \QtyRef{magnetic_vector_potential}, \ConstRef{vacuum_speed_of_light}}
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\desc[german]{Hamiltonian eines Teilchens im elektromagnetischen Feld}{In der \fRef{ed:em:maxwell:gauge:coulomb}}{}
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\eq{
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\hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2
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}
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\end{formula}
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\Subsection{maxwell}
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\desc{Maxwell-Equations}{}{}
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\desc[german]{Maxwell-Gleichungen}{}{}
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\begin{formula}{vacuum}
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\desc{Vacuum}{microscopic formulation}{}
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\desc[german]{Vakuum}{Mikroskopische Formulierung}{}
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\eq{
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\Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
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\Div \vec{B} &= 0 \\
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\Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
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\Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t}
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}
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\end{formula}
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\begin{formula}{material}
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\desc{Matter}{Macroscopic formulation}{}
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\desc[german]{Materie}{Makroskopische Formulierung}{}
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\eq{
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\Div \vec{D} &= \rho_\text{el} \\
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\Div \vec{B} &= 0 \\
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\Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
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\Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
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}
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\end{formula}
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\Subsubsection{gauge}
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\desc{Gauges}{}{}
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\desc[german]{Eichungen}{}{}
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\begin{formula}{coulomb}
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\desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
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\desc[german]{Coulomb-Eichung}{}{}
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\eq{
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\Div \vec{A} = 0
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}
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\end{formula}
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\TODO{Polarization}
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\Subsection{induction}
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\desc{Induction}{}{}
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\desc[german]{Induktion}{}{}
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\begin{formula}{farady_law}
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\desc{Faraday's law of induction}{}{}
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\desc[german]{Faradaysche Induktionsgesetz}{}{}
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\eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
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\end{formula}
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\begin{formula}{lenz}
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\desc{Lenz's law}{}{}
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\desc[german]{Lenzsche Regel}{}{}
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\ttxt{
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\eng{
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Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
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}
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\ger{
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Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
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}
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}
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\end{formula}
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