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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Flussdichte</span></h1>
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<p>Die <b>Flussdichte</b> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ef40edff397a115ecdce7d3518001dfcc7f37d9e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}" loading="lazy"></span> ist ein <a href="Vektorfeld" title="Vektorfeld">Vektorfeld</a>, welches die Menge einer <a href="Physikalische_Gr%C3%B6%C3%9Fe" title="Physikalische Größe">physikalischen Größe</a> beschreibt, die pro Flächenelement <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} {\vec {A}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathrm {d} {\vec {A}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d9f9388557a681a60c4b6e29cd5e877b13d41622.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.036ex; height:3.009ex;" alt="{\displaystyle \mathrm {d} {\vec {A}}}" loading="lazy"></span> durch eine Probefläche <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle S}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4611d85173cd3b508e67077d4a1252c9c05abca2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" loading="lazy"></span> hindurchfließt. Die Gesamtmenge wird als <a href="Fluss_(Physik)" title="Fluss (Physik)">Fluss</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Φ<!-- Φ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/aed80a2011a3912b028ba32a52dfa57165455f24.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }" loading="lazy"></span> bezeichnet, somit ergibt sich:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi =\int _{S}{\vec {F}}\mathrm {\cdot } \mathrm {d} {\vec {A}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Φ<!-- Φ --></mi>
<mo>=</mo>
<msub>
<mo>∫<!-- ∫ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>S</mi>
</mrow>
</msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>⋅<!-- ⋅ --></mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Phi =\int _{S}{\vec {F}}\mathrm {\cdot } \mathrm {d} {\vec {A}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/da430c420ac83a9c9d81d8bc15cb6fbeceee3728.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.202ex; height:5.676ex;" alt="{\displaystyle \Phi =\int _{S}{\vec {F}}\mathrm {\cdot } \mathrm {d} {\vec {A}}}" loading="lazy"></span></dd></dl>
<p>Im Allgemeinen gilt:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A}}\cos(\theta ){\vec {e}}_{F}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mi mathvariant="normal">Φ<!-- Φ --></mi>
</mrow>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mi>A</mi>
</mrow>
</mfrac>
</mrow>
<mi>cos</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mi>θ<!-- θ --></mi>
<mo stretchy="false">)</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>e</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>F</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A}}\cos(\theta ){\vec {e}}_{F}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0a4994187e2db5bb6656da996a0710f21f6101e9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.825ex; height:5.509ex;" alt="{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A}}\cos(\theta ){\vec {e}}_{F}}" loading="lazy"></span></dd></dl>
<p>wobei <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\arccos \left({\frac {{\vec {F}}\mathrm {d} {\vec {A}}}{|{\vec {F}}|\cdot |\mathrm {d} {\vec {A}}|}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>θ<!-- θ --></mi>
<mo>=</mo>
<mi>arccos</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mrow>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \theta =\arccos \left({\frac {{\vec {F}}\mathrm {d} {\vec {A}}}{|{\vec {F}}|\cdot |\mathrm {d} {\vec {A}}|}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e924791d2e8190b3069a364b9a792609203ec386.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:23.997ex; height:7.676ex;" alt="{\displaystyle \theta =\arccos \left({\frac {{\vec {F}}\mathrm {d} {\vec {A}}}{|{\vec {F}}|\cdot |\mathrm {d} {\vec {A}}|}}\right)}" loading="lazy"></span> der Winkel zwischen <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ef40edff397a115ecdce7d3518001dfcc7f37d9e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}" loading="lazy"></span> und der Senkrechten <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} {\vec {A}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathrm {d} {\vec {A}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d9f9388557a681a60c4b6e29cd5e877b13d41622.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.036ex; height:3.009ex;" alt="{\displaystyle \mathrm {d} {\vec {A}}}" loading="lazy"></span> des Flächenelements <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} {\vec {A}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathrm {d} {\vec {A}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d9f9388557a681a60c4b6e29cd5e877b13d41622.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.036ex; height:3.009ex;" alt="{\displaystyle \mathrm {d} {\vec {A}}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {e}}_{F}={\frac {\vec {F}}{F}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>e</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>F</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
<mi>F</mi>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {e}}_{F}={\frac {\vec {F}}{F}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5cb657f3795f594f12e9dcce8bc7f254465026c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.392ex; height:6.009ex;" alt="{\displaystyle {\vec {e}}_{F}={\frac {\vec {F}}{F}}}" loading="lazy"></span> der <a href="Einheitsvektor" title="Einheitsvektor">Einheitsvektor</a> in Richtung von <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>F</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/545fd099af8541605f7ee55f08225526be88ce57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}" loading="lazy"></span> ist.
</p><p>Falls die Fläche senkrecht zur Flussrichtung orientiert ist, gilt:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A_{\perp }}}\cdot {\vec {e}}_{F}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>F</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mi mathvariant="normal">Φ<!-- Φ --></mi>
</mrow>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<msub>
<mi>A</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>⊥<!-- ⊥ --></mo>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mo>⋅<!-- ⋅ --></mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>e</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>F</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A_{\perp }}}\cdot {\vec {e}}_{F}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/932b3e0de8044dbc900f1535a881d4e624d54adc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.617ex; height:5.843ex;" alt="{\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A_{\perp }}}\cdot {\vec {e}}_{F}}" loading="lazy"></span></dd></dl>
<p>Im Englischen ist neben <i>flux density</i> auch die Bezeichnung <i>fluence rate</i> („Fluenzrate“) gebräuchlich.
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<div class="mw-heading mw-heading2"><h2 id="Beispiele">Beispiele</h2></div>
<ul><li><a href="Elektrische_Flussdichte" title="Elektrische Flussdichte">Elektrische Flussdichte</a> des <a href="Elektrisches_Feld" title="Elektrisches Feld">elektrischen Feldes</a></li>
<li><a href="Magnetische_Flussdichte" title="Magnetische Flussdichte">Magnetische Flussdichte</a> des <a href="Magnetisches_Feld" class="mw-redirect" title="Magnetisches Feld">magnetischen Feldes</a></li>
<li><a href="Impulsstromdichte" title="Impulsstromdichte">Impulsstromdichte</a></li>
<li><a href="Elektrische_Stromdichte" title="Elektrische Stromdichte">Elektrische Stromdichte</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>
<ul><li><a href="Fluenz" title="Fluenz">Fluenz</a> (Teilchen pro Fläche)</li>
<li>elektrische <a href="Stromdichte" class="mw-redirect" title="Stromdichte">Stromdichte</a>, <a href="Dielektrikum" title="Dielektrikum">Dielektrikum</a></li>
<li>Strahlungsstromdichte (<a href="Bestrahlungsst%C3%A4rke" title="Bestrahlungsstärke">Bestrahlungsstärke</a>), Lichtstromdichte (<a href="Beleuchtungsst%C3%A4rke" title="Beleuchtungsstärke">Beleuchtungsstärke</a>)</li>
<li><a href="Teilchenstromdichte" title="Teilchenstromdichte">Teilchenstromdichte</a></li>
<li><a href="Neutronenflussdichte" class="mw-redirect" title="Neutronenflussdichte">Neutronenflussdichte</a></li></ul>
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Normdaten (Sachbegriff): <a href="Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4627766-3">4627766-3</a></span> </div>
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