Jump to navigation Jump to search

General

Display information for equation id:math.244757.20 on revision:244757

* Page found: Maxwell stress tensor (eq math.244757.20)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 09fccec47018501be53791cd70dcc03c

TeX (original user input):

\overset{\leftrightarrow  }{ \mathbf{\sigma} } = \frac{1}{4\pi} \left[ \mathbf{E}\otimes\mathbf{E} + \mathbf{H}\otimes\mathbf{H} - \frac{E^2+H^2 }{2} (\mathbf{\hat x}\otimes\mathbf{\hat x} + \mathbf{\hat y}\otimes\mathbf{\hat y} + \mathbf{\hat z}\otimes\mathbf{\hat z}) \right]

LaTeXML (experimental; uses MathML) rendering

MathML (13.258 KB / 1.856 KB) :

σ = 1 4 π [ 𝐄 𝐄 + 𝐇 𝐇 - E 2 + H 2 2 ( 𝐱 ^ 𝐱 ^ + 𝐲 ^ 𝐲 ^ + 𝐳 ^ 𝐳 ^ ) ] 𝜎 1 4 𝜋 delimited-[] tensor-product 𝐄 𝐄 tensor-product 𝐇 𝐇 superscript 𝐸 2 superscript 𝐻 2 2 tensor-product ^ 𝐱 ^ 𝐱 tensor-product ^ 𝐲 ^ 𝐲 tensor-product ^ 𝐳 ^ 𝐳 {\displaystyle{\overset{\leftrightarrow}{{\mathbf{\sigma}}}}={\frac{1}{4\pi}}% \left[{\mathbf{E}}\otimes{\mathbf{E}}+{\mathbf{H}}\otimes{\mathbf{H}}-{\frac{E% ^{2}+H^{2}}{2}}({\mathbf{{\hat{x}}}}\otimes{\mathbf{{\hat{x}}}}+{\mathbf{{\hat% {y}}}}\otimes{\mathbf{{\hat{y}}}}+{\mathbf{{\hat{z}}}}\otimes{\mathbf{{\hat{z}% }}})\right]}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\overset{\leftrightarrow}{{\mathbf{\sigma}}}}={\frac{1}{4\pi}}%&#10;\left[{\mathbf{E}}\otimes{\mathbf{E}}+{\mathbf{H}}\otimes{\mathbf{H}}-{\frac{E%&#10;^{2}+H^{2}}{2}}({\mathbf{{\hat{x}}}}\otimes{\mathbf{{\hat{x}}}}+{\mathbf{{\hat%&#10;{y}}}}\otimes{\mathbf{{\hat{y}}}}+{\mathbf{{\hat{z}}}}\otimes{\mathbf{{\hat{z}%&#10;}}})\right]}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
      <mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
        <mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">σ</mi>
        <mo id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml"></mo>
      </mover>
      <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
      <mrow id="p1.1.m1.1.28.1" xref="p1.1.m1.1.28.1.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
          <mfrac id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">
            <mn id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">1</mn>
            <mrow id="p1.1.m1.1.3.3" xref="p1.1.m1.1.3.3.cmml">
              <mn id="p1.1.m1.1.3.3.1" xref="p1.1.m1.1.3.3.1.cmml">4</mn>
              <mo id="p1.1.m1.1.3.3.3" xref="p1.1.m1.1.3.3.3.cmml"></mo>
              <mi id="p1.1.m1.1.3.3.2" xref="p1.1.m1.1.3.3.2.cmml">π</mi>
            </mrow>
          </mfrac>
        </mstyle>
        <mo id="p1.1.m1.1.28.1.1" xref="p1.1.m1.1.28.1.1.cmml"></mo>
        <mrow id="p1.1.m1.1.28.1.2" xref="p1.1.m1.1.28.1.2.1.cmml">
          <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.28.1.2.1.1.cmml">[</mo>
          <mrow id="p1.1.m1.1.28.1.2.2" xref="p1.1.m1.1.28.1.2.2.cmml">
            <mrow id="p1.1.m1.1.28.1.2.2.1" xref="p1.1.m1.1.28.1.2.2.1.cmml">
              <mrow id="p1.1.m1.1.28.1.2.2.1.1" xref="p1.1.m1.1.28.1.2.2.1.1.cmml">
                <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">𝐄</mi>
                <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml"></mo>
                <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">𝐄</mi>
              </mrow>
              <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">+</mo>
              <mrow id="p1.1.m1.1.28.1.2.2.1.2" xref="p1.1.m1.1.28.1.2.2.1.2.cmml">
                <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">𝐇</mi>
                <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml"></mo>
                <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">𝐇</mi>
              </mrow>
            </mrow>
            <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">-</mo>
            <mrow id="p1.1.m1.1.28.1.2.2.2" xref="p1.1.m1.1.28.1.2.2.2.cmml">
              <mstyle displaystyle="true" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
                <mfrac id="p1.1.m1.1.13a" xref="p1.1.m1.1.13.cmml">
                  <mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
                    <msup id="p1.1.m1.1.13.2.6" xref="p1.1.m1.1.13.2.6.cmml">
                      <mi id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">E</mi>
                      <mn id="p1.1.m1.1.13.2.2.1" xref="p1.1.m1.1.13.2.2.1.cmml">2</mn>
                    </msup>
                    <mo id="p1.1.m1.1.13.2.3" xref="p1.1.m1.1.13.2.3.cmml">+</mo>
                    <msup id="p1.1.m1.1.13.2.7" xref="p1.1.m1.1.13.2.7.cmml">
                      <mi id="p1.1.m1.1.13.2.4" xref="p1.1.m1.1.13.2.4.cmml">H</mi>
                      <mn id="p1.1.m1.1.13.2.5.1" xref="p1.1.m1.1.13.2.5.1.cmml">2</mn>
                    </msup>
                  </mrow>
                  <mn id="p1.1.m1.1.13.3" xref="p1.1.m1.1.13.3.cmml">2</mn>
                </mfrac>
              </mstyle>
              <mo id="p1.1.m1.1.28.1.2.2.2.1" xref="p1.1.m1.1.28.1.2.2.2.1.cmml"></mo>
              <mrow id="p1.1.m1.1.28.1.2.2.2.2" xref="p1.1.m1.1.28.1.2.2.2.2.2.cmml">
                <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.28.1.2.2.2.2.2.cmml">(</mo>
                <mrow id="p1.1.m1.1.28.1.2.2.2.2.2" xref="p1.1.m1.1.28.1.2.2.2.2.2.cmml">
                  <mrow id="p1.1.m1.1.28.1.2.2.2.2.2.1" xref="p1.1.m1.1.28.1.2.2.2.2.2.1.cmml">
                    <mover accent="true" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
                      <mi id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">𝐱</mi>
                      <mo stretchy="false" id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">^</mo>
                    </mover>
                    <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml"></mo>
                    <mover accent="true" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
                      <mi id="p1.1.m1.1.17.2" xref="p1.1.m1.1.17.2.cmml">𝐱</mi>
                      <mo stretchy="false" id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">^</mo>
                    </mover>
                  </mrow>
                  <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">+</mo>
                  <mrow id="p1.1.m1.1.28.1.2.2.2.2.2.2" xref="p1.1.m1.1.28.1.2.2.2.2.2.2.cmml">
                    <mover accent="true" id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
                      <mi id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.cmml">𝐲</mi>
                      <mo stretchy="false" id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">^</mo>
                    </mover>
                    <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml"></mo>
                    <mover accent="true" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
                      <mi id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.cmml">𝐲</mi>
                      <mo stretchy="false" id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">^</mo>
                    </mover>
                  </mrow>
                  <mo id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">+</mo>
                  <mrow id="p1.1.m1.1.28.1.2.2.2.2.2.3" xref="p1.1.m1.1.28.1.2.2.2.2.2.3.cmml">
                    <mover accent="true" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
                      <mi id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">𝐳</mi>
                      <mo stretchy="false" id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">^</mo>
                    </mover>
                    <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml"></mo>
                    <mover accent="true" id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">
                      <mi id="p1.1.m1.1.25.2" xref="p1.1.m1.1.25.2.cmml">𝐳</mi>
                      <mo stretchy="false" id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">^</mo>
                    </mover>
                  </mrow>
                </mrow>
                <mo stretchy="false" id="p1.1.m1.1.26" xref="p1.1.m1.1.28.1.2.2.2.2.2.cmml">)</mo>
              </mrow>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.28.1.2.1.1.cmml">]</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
        <eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
        <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
          <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1"></ci>
          <ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">𝜎</ci>
        </apply>
        <apply id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28.1">
          <times id="p1.1.m1.1.28.1.1.cmml" xref="p1.1.m1.1.28.1.1"/>
          <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
            <divide id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3"/>
            <cn type="integer" id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">1</cn>
            <apply id="p1.1.m1.1.3.3.cmml" xref="p1.1.m1.1.3.3">
              <times id="p1.1.m1.1.3.3.3.cmml" xref="p1.1.m1.1.3.3.3"/>
              <cn type="integer" id="p1.1.m1.1.3.3.1.cmml" xref="p1.1.m1.1.3.3.1">4</cn>
              <ci id="p1.1.m1.1.3.3.2.cmml" xref="p1.1.m1.1.3.3.2">𝜋</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.28.1.2.1.cmml" xref="p1.1.m1.1.28.1.2">
            <csymbol cd="latexml" id="p1.1.m1.1.28.1.2.1.1.cmml" xref="p1.1.m1.1.4">delimited-[]</csymbol>
            <apply id="p1.1.m1.1.28.1.2.2.cmml" xref="p1.1.m1.1.28.1.2.2">
              <minus id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
              <apply id="p1.1.m1.1.28.1.2.2.1.cmml" xref="p1.1.m1.1.28.1.2.2.1">
                <plus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
                <apply id="p1.1.m1.1.28.1.2.2.1.1.cmml" xref="p1.1.m1.1.28.1.2.2.1.1">
                  <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">tensor-product</csymbol>
                  <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝐄</ci>
                  <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝐄</ci>
                </apply>
                <apply id="p1.1.m1.1.28.1.2.2.1.2.cmml" xref="p1.1.m1.1.28.1.2.2.1.2">
                  <csymbol cd="latexml" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">tensor-product</csymbol>
                  <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝐇</ci>
                  <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝐇</ci>
                </apply>
              </apply>
              <apply id="p1.1.m1.1.28.1.2.2.2.cmml" xref="p1.1.m1.1.28.1.2.2.2">
                <times id="p1.1.m1.1.28.1.2.2.2.1.cmml" xref="p1.1.m1.1.28.1.2.2.2.1"/>
                <apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
                  <divide id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13"/>
                  <apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
                    <plus id="p1.1.m1.1.13.2.3.cmml" xref="p1.1.m1.1.13.2.3"/>
                    <apply id="p1.1.m1.1.13.2.6.cmml" xref="p1.1.m1.1.13.2.6">
                      <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.6.1.cmml" xref="p1.1.m1.1.13.2.6">superscript</csymbol>
                      <ci id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1">𝐸</ci>
                      <cn type="integer" id="p1.1.m1.1.13.2.2.1.cmml" xref="p1.1.m1.1.13.2.2.1">2</cn>
                    </apply>
                    <apply id="p1.1.m1.1.13.2.7.cmml" xref="p1.1.m1.1.13.2.7">
                      <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.7.1.cmml" xref="p1.1.m1.1.13.2.7">superscript</csymbol>
                      <ci id="p1.1.m1.1.13.2.4.cmml" xref="p1.1.m1.1.13.2.4">𝐻</ci>
                      <cn type="integer" id="p1.1.m1.1.13.2.5.1.cmml" xref="p1.1.m1.1.13.2.5.1">2</cn>
                    </apply>
                  </apply>
                  <cn type="integer" id="p1.1.m1.1.13.3.cmml" xref="p1.1.m1.1.13.3">2</cn>
                </apply>
                <apply id="p1.1.m1.1.28.1.2.2.2.2.2.cmml" xref="p1.1.m1.1.28.1.2.2.2.2">
                  <plus id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"/>
                  <apply id="p1.1.m1.1.28.1.2.2.2.2.2.1.cmml" xref="p1.1.m1.1.28.1.2.2.2.2.2.1">
                    <csymbol cd="latexml" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">tensor-product</csymbol>
                    <apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
                      <ci id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">^</ci>
                      <ci id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">𝐱</ci>
                    </apply>
                    <apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
                      <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">^</ci>
                      <ci id="p1.1.m1.1.17.2.cmml" xref="p1.1.m1.1.17.2">𝐱</ci>
                    </apply>
                  </apply>
                  <apply id="p1.1.m1.1.28.1.2.2.2.2.2.2.cmml" xref="p1.1.m1.1.28.1.2.2.2.2.2.2">
                    <csymbol cd="latexml" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">tensor-product</csymbol>
                    <apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
                      <ci id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">^</ci>
                      <ci id="p1.1.m1.1.19.2.cmml" xref="p1.1.m1.1.19.2">𝐲</ci>
                    </apply>
                    <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
                      <ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">^</ci>
                      <ci id="p1.1.m1.1.21.2.cmml" xref="p1.1.m1.1.21.2">𝐲</ci>
                    </apply>
                  </apply>
                  <apply id="p1.1.m1.1.28.1.2.2.2.2.2.3.cmml" xref="p1.1.m1.1.28.1.2.2.2.2.2.3">
                    <csymbol cd="latexml" id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">tensor-product</csymbol>
                    <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
                      <ci id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">^</ci>
                      <ci id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">𝐳</ci>
                    </apply>
                    <apply id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">
                      <ci id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">^</ci>
                      <ci id="p1.1.m1.1.25.2.cmml" xref="p1.1.m1.1.25.2">𝐳</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\overset{\leftrightarrow}{{\mathbf{\sigma}}}}={\frac{1}{4\pi}}%
\left[{\mathbf{E}}\otimes{\mathbf{E}}+{\mathbf{H}}\otimes{\mathbf{H}}-{\frac{E%
^{2}+H^{2}}{2}}({\mathbf{{\hat{x}}}}\otimes{\mathbf{{\hat{x}}}}+{\mathbf{{\hat%
{y}}}}\otimes{\mathbf{{\hat{y}}}}+{\mathbf{{\hat{z}}}}\otimes{\mathbf{{\hat{z}%
}}})\right]}</annotation>
  </semantics>
</math>

SVG (16.744 KB / 5.356 KB) :

ModifyingAbove sigma With left-right-arrow equals StartFraction 1 Over 4 times pi EndFraction times left-bracket bold upper E circled-times bold upper E plus bold upper H circled-times bold upper H minus StartFraction upper E squared plus upper H squared Over 2 EndFraction times left-parenthesis ModifyingAbove bold x With caret circled-times ModifyingAbove bold x With caret plus ModifyingAbove bold y With caret circled-times ModifyingAbove bold y With caret plus ModifyingAbove bold z With caret circled-times ModifyingAbove bold z With caret right-parenthesis right-bracket

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (4.719 KB / 688 B) :

σ = 1 4 π [ E E + H H E 2 + H 2 2 ( x ^ x ^ + y ^ y ^ + z ^ z ^ ) ] {\displaystyle {\overset {\leftrightarrow }{\mathbf {\sigma } }}={\frac {1}{4\pi }}\left[\mathbf {E} \otimes \mathbf {E} +\mathbf {H} \otimes \mathbf {H} -{\frac {E^{2}+H^{2}}{2}}(\mathbf {\hat {x}} \otimes \mathbf {\hat {x}} +\mathbf {\hat {y}} \otimes \mathbf {\hat {y}} +\mathbf {\hat {z}} \otimes \mathbf {\hat {z}} )\right]}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\overset {\leftrightarrow }{\mathbf {\sigma } }}={\frac {1}{4\pi }}\left[\mathbf {E} \otimes \mathbf {E} +\mathbf {H} \otimes \mathbf {H} -{\frac {E^{2}+H^{2}}{2}}(\mathbf {\hat {x}} \otimes \mathbf {\hat {x}} +\mathbf {\hat {y}} \otimes \mathbf {\hat {y}} +\mathbf {\hat {z}} \otimes \mathbf {\hat {z}} )\right]}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mover>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>&#x03C3;<!-- σ --></mi>
            </mrow>
            <mo stretchy="false">&#x2194;<!-- ↔ --></mo>
          </mover>
        </mrow>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mn>1</mn>
            <mrow>
              <mn>4</mn>
              <mi>&#x03C0;<!-- π --></mi>
            </mrow>
          </mfrac>
        </mrow>
        <mrow>
          <mo>[</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="bold">E</mi>
            </mrow>
            <mo>&#x2297;<!-- ⊗ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="bold">E</mi>
            </mrow>
            <mo>+</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="bold">H</mi>
            </mrow>
            <mo>&#x2297;<!-- ⊗ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="bold">H</mi>
            </mrow>
            <mo>&#x2212;<!-- − --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mfrac>
                <mrow>
                  <msup>
                    <mi>E</mi>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>+</mo>
                  <msup>
                    <mi>H</mi>
                    <mrow class="MJX-TeXAtom-ORD">
                      <mn>2</mn>
                    </mrow>
                  </msup>
                </mrow>
                <mn>2</mn>
              </mfrac>
            </mrow>
            <mo stretchy="false">(</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">x</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo>&#x2297;<!-- ⊗ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">x</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo>+</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">y</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo>&#x2297;<!-- ⊗ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">y</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo>+</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">z</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo>&#x2297;<!-- ⊗ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi mathvariant="bold">z</mi>
                  <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mo stretchy="false">)</mo>
          </mrow>
          <mo>]</mo>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\overset {\leftrightarrow }{\mathbf {\sigma } }}={\frac {1}{4\pi }}\left[\mathbf {E} \otimes \mathbf {E} +\mathbf {H} \otimes \mathbf {H} -{\frac {E^{2}+H^{2}}{2}}(\mathbf {\hat {x}} \otimes \mathbf {\hat {x}} +\mathbf {\hat {y}} \otimes \mathbf {\hat {y}} +\mathbf {\hat {z}} \otimes \mathbf {\hat {z}} )\right]}</annotation>
  </semantics>
</math>

SVG (12.46 KB / 4.81 KB) :

{\displaystyle {\overset {\leftrightarrow }{\mathbf {\sigma } }}={\frac {1}{4\pi }}\left[\mathbf {E} \otimes \mathbf {E} +\mathbf {H} \otimes \mathbf {H} -{\frac {E^{2}+H^{2}}{2}}(\mathbf {\hat {x}} \otimes \mathbf {\hat {x}} +\mathbf {\hat {y}} \otimes \mathbf {\hat {y}} +\mathbf {\hat {z}} \otimes \mathbf {\hat {z}} )\right]}

PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Maxwell stress tensor page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results