124 lines
5.4 KiB
TeX
124 lines
5.4 KiB
TeX
\Section{mag}
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\desc{Magnetic field}{}{}
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\desc[german]{Magnetfeld}{}{}
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\begin{formula}{magnetic_flux}
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\desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
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\desc[german]{Magnetischer Fluss}{}{}
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\quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
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\eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
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\end{formula}
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\begin{formula}{magnetic_flux_density}
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\desc{Magnetic flux density}{Defined by \fRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}}
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\desc[german]{Magnetische Flussdichte}{Definiert über \fRef{ed:mag:lorentz}}{}
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\quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
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\eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
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\end{formula}
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\begin{formula}{magnetic_vector_potential}
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\desc{Magnetic vector potential}{}{}
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\desc[german]{Magnetisches Vektorpotential}{}{}
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\quantity{\vec{A}}{\tesla\m=\volt\s\per\m=\kg\m\per\s^2\ampere}{ievs}
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\eq{\Rot\vec{A}(\vecr) = \vec{B}(\vecr)}
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\end{formula}
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\begin{formula}{magnetic_field_intensity}
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\desc{Magnetic field intensity}{}{}
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\desc[german]{Magnetische Feldstärke}{}{}
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\quantity{\vec{H}}{\ampere\per\m}{vector}
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\eq{
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\vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M}
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}
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\end{formula}
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\begin{formula}{lorentz}
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\desc{Lorentz force law}{Force on charged particle}{}
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\desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{}
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\eq{
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\vec{F} = q \vec{\E} + q \vec{v}\times\vec{B}
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}
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\end{formula}
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\begin{formula}{magnetic_permeability}
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\desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
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\desc[german]{Magnetisch Permeabilität}{}{}
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\quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
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\eq{\mu=\frac{B}{H}}
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\end{formula}
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\begin{formula}{magnetic_vacuum_permeability}
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\desc{Magnetic vauum permeability}{}{}
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\desc[german]{Magnetische Vakuumpermeabilität}{}{}
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\constant{\mu_0}{exp}{
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\val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
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}
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\end{formula}
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\begin{formula}{relative_permeability}
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\desc{Relative permeability}{}{}
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\desc[german]{Realtive Permeabilität}{}{}
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\eq{
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\mu_\txr = \frac{\mu}{\mu_0}
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}
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\hiddenQuantity{\mu_\txr}{ }{}
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\end{formula}
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\begin{formula}{gauss_law}
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\desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
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\desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
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\eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
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\end{formula}
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\begin{formula}{magnetization}
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\desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
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\desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
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\quantity{\vec{M}}{\ampere\per\m}{vector}
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\eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
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\end{formula}
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\begin{formula}{magnetic_moment}
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\desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
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\desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
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\quantity{\vec{m}}{\ampere\m^2}{vector}
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\end{formula}
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\begin{formula}{angular_torque}
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\desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
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\desc[german]{Drehmoment}{}{}
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\eq{\vec{\tau} = \vec{m} \times \vec{B}}
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\end{formula}
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\begin{formula}{magnetic_susceptibility}
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\desc{Susceptibility}{}{$\mu_\txr$ \fRef{ed:mag:relative_permeability}}
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\desc[german]{Suszeptibilität}{}{}
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\eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
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\hiddenQuantity{\chi}{}{}
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\end{formula}
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\Subsection{materials}
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\desc{Magnetic materials}{}{}
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\desc[german]{Magnetische Materialien}{}{}
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\begin{formula}{paramagnetism}
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\desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
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\desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
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\eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
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\end{formula}
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\begin{formula}{diamagnetism}
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\desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
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\desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
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\eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
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\end{formula}
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\begin{formula}{ferromagnetism}
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\desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
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\desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
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\eq{
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\mu_\txr \gg 1
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}
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\end{formula}
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