Jump to navigation Jump to search

General

Display information for equation id:math.244757.3 on revision:244757

* Page found: Maxwell stress tensor (eq math.244757.3)

(force rerendering)

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

Occurrences on the following pages:

Hash: a999cd7194e269954472e6e134287e9f

TeX (original user input):

\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}} {\partial t}\

LaTeXML (experimental; uses MathML) rendering

MathML (5.758 KB / 1.052 KB) :

× 𝐁 = μ 0 𝐉 + μ 0 ϵ 0 𝐄 t 𝐁 subscript 𝜇 0 𝐉 subscript 𝜇 0 subscript italic-ϵ 0 𝐄 𝑡 {\displaystyle\nabla\times{\mathbf{B}}=\mu_{0}{\mathbf{J}}+\mu_{0}\epsilon_{0}% {\frac{\partial{\mathbf{E}}}{\partial t}}\ }
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\nabla\times{\mathbf{B}}=\mu_{0}{\mathbf{J}}+\mu_{0}\epsilon_{0}%&#10;{\frac{\partial{\mathbf{E}}}{\partial t}}\ }" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
      <mrow id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
        <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml"></mo>
        <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">×</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">𝐁</mi>
      </mrow>
      <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">=</mo>
      <mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
        <mrow id="p1.1.m1.1.15.2.1" xref="p1.1.m1.1.15.2.1.cmml">
          <msub id="p1.1.m1.1.15.2.1.2" xref="p1.1.m1.1.15.2.1.2.cmml">
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">μ</mi>
            <mn id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.15.2.1.1" xref="p1.1.m1.1.15.2.1.1.cmml"></mo>
          <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">𝐉</mi>
        </mrow>
        <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">+</mo>
        <mrow id="p1.1.m1.1.15.2.2" xref="p1.1.m1.1.15.2.2.cmml">
          <msub id="p1.1.m1.1.15.2.2.2" xref="p1.1.m1.1.15.2.2.2.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">μ</mi>
            <mn id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.15.2.2.1" xref="p1.1.m1.1.15.2.2.1.cmml"></mo>
          <msub id="p1.1.m1.1.15.2.2.3" xref="p1.1.m1.1.15.2.2.3.cmml">
            <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">ϵ</mi>
            <mn id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.15.2.2.1a" xref="p1.1.m1.1.15.2.2.1.cmml"></mo>
          <mpadded width="+5pt" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
            <mstyle displaystyle="true" id="p1.1.m1.1.13a" xref="p1.1.m1.1.13.cmml">
              <mfrac id="p1.1.m1.1.13b" xref="p1.1.m1.1.13.cmml">
                <mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
                  <mo id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml"></mo>
                  <mo id="p1.1.m1.1.13.2a" xref="p1.1.m1.1.13.2.cmml"></mo>
                  <mi id="p1.1.m1.1.13.2.2" xref="p1.1.m1.1.13.2.2.cmml">𝐄</mi>
                </mrow>
                <mrow id="p1.1.m1.1.13.3" xref="p1.1.m1.1.13.3.cmml">
                  <mo id="p1.1.m1.1.13.3.1" xref="p1.1.m1.1.13.3.1.cmml"></mo>
                  <mo id="p1.1.m1.1.13.3a" xref="p1.1.m1.1.13.3.cmml"></mo>
                  <mi id="p1.1.m1.1.13.3.2" xref="p1.1.m1.1.13.3.2.cmml">t</mi>
                </mrow>
              </mfrac>
            </mstyle>
          </mpadded>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
        <eq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
        <apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
          <times id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"></ci>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝐁</ci>
        </apply>
        <apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
          <plus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
          <apply id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2.1">
            <times id="p1.1.m1.1.15.2.1.1.cmml" xref="p1.1.m1.1.15.2.1.1"/>
            <apply id="p1.1.m1.1.15.2.1.2.cmml" xref="p1.1.m1.1.15.2.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.1.2.1.cmml" xref="p1.1.m1.1.15.2.1.2">subscript</csymbol>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝜇</ci>
              <cn type="integer" id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">0</cn>
            </apply>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝐉</ci>
          </apply>
          <apply id="p1.1.m1.1.15.2.2.cmml" xref="p1.1.m1.1.15.2.2">
            <times id="p1.1.m1.1.15.2.2.1.cmml" xref="p1.1.m1.1.15.2.2.1"/>
            <apply id="p1.1.m1.1.15.2.2.2.cmml" xref="p1.1.m1.1.15.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.2.1.cmml" xref="p1.1.m1.1.15.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝜇</ci>
              <cn type="integer" id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">0</cn>
            </apply>
            <apply id="p1.1.m1.1.15.2.2.3.cmml" xref="p1.1.m1.1.15.2.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.3.1.cmml" xref="p1.1.m1.1.15.2.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">italic-ϵ</ci>
              <cn type="integer" id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">0</cn>
            </apply>
            <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">
                <partialdiff id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1"/>
                <ci id="p1.1.m1.1.13.2.2.cmml" xref="p1.1.m1.1.13.2.2">𝐄</ci>
              </apply>
              <apply id="p1.1.m1.1.13.3.cmml" xref="p1.1.m1.1.13.3">
                <partialdiff id="p1.1.m1.1.13.3.1.cmml" xref="p1.1.m1.1.13.3.1"/>
                <ci id="p1.1.m1.1.13.3.2.cmml" xref="p1.1.m1.1.13.3.2">𝑡</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\nabla\times{\mathbf{B}}=\mu_{0}{\mathbf{J}}+\mu_{0}\epsilon_{0}%
{\frac{\partial{\mathbf{E}}}{\partial t}}\ }</annotation>
  </semantics>
</math>

SVG (8.536 KB / 3.094 KB) :

nabla times bold upper B equals mu 0 times bold upper J plus mu 0 times epsilon 0 times StartFraction partial-differential bold upper E Over partial-differential t EndFraction

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

MathML (1.752 KB / 491 B) :

× B = μ 0 J + μ 0 ϵ 0 E t   {\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\ }
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\ }">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
        <mo>&#x00D7;<!-- × --></mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold">B</mi>
        </mrow>
        <mo>=</mo>
        <msub>
          <mi>&#x03BC;<!-- μ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
        </msub>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold">J</mi>
        </mrow>
        <mo>+</mo>
        <msub>
          <mi>&#x03BC;<!-- μ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
        </msub>
        <msub>
          <mi>&#x03F5;<!-- ϵ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
        </msub>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mrow>
              <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
              <mrow class="MJX-TeXAtom-ORD">
                <mi mathvariant="bold">E</mi>
              </mrow>
            </mrow>
            <mrow>
              <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
              <mi>t</mi>
            </mrow>
          </mfrac>
        </mrow>
        <mtext>&#xA0;</mtext>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\ }</annotation>
  </semantics>
</math>

SVG (6.651 KB / 2.847 KB) :

{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\ }

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