Commit b6ec4922 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.en.md

parent e778aec5
Pipeline #21658 canceled with stage
...@@ -240,7 +240,7 @@ _thus revolutionizing physics._ ...@@ -240,7 +240,7 @@ _thus revolutionizing physics._
with orientation compatible with that of $`S`$ according to the right-hand rule: with orientation compatible with that of $`S`$ according to the right-hand rule:
* $`\forall \overrightarrow{r},\;`$ *$`\mathbf{\overrightarrow{\text{curl}} \,\overrightarrow{E} = -\dfrac{\partial \overrightarrow{B}}{\partial t}}`$* * $`\forall \overrightarrow{r},\;`$ *$`\mathbf{\overrightarrow{\text{curl}} \,\overrightarrow{E} = -\dfrac{\partial \overrightarrow{B}}{\partial t}}`$*
$`\Longrightarrow \iint_S \overrightarrow{\text{curl}} \,\overrightarrow{E}\cdot\overrightarrow{dS} = \iint_S\Big(-\dfrac{\partial\overrightarrow{B}}{\partial t}\cdot\overrightarrow{dS}\Big)`$ $`\Longrightarrow \iint_S \overrightarrow{\text{curl}} \,\overrightarrow{E}\cdot\overrightarrow{dS} = \iint_S\Big(-\dfrac{\partial\overrightarrow{B}}{\partial t}\cdot\overrightarrow{dS}\Big)`$
<br> <br>
* $`\left.\begin{array}{l} * $`\left.\begin{array}{l}
...@@ -250,7 +250,7 @@ _thus revolutionizing physics._ ...@@ -250,7 +250,7 @@ _thus revolutionizing physics._
\text{does not matter} \text{does not matter}
\end{array}\right\}`$ \end{array}\right\}`$
$`\Longrightarrow`$ $`\Longrightarrow`$
$`\iint_S \overrightarrow{\text{curl}} \,\overrightarrow{E}\cdot\overrightarrow{dS} = -\dfrac{d}{dt}\Big(\iint_S\overrightarrow{B}\cdot\overrightarrow{dS}\Big)`$ $`\iint_S \overrightarrow{\text{curl}} \,\overrightarrow{E}\cdot\overrightarrow{dS} = -\dfrac{d}{dt}\Big(\iint_S\overrightarrow{B}\cdot\overrightarrow{dS}\Big)`$
<br> <br>
* $`\left.\begin{array}{l} * $`\left.\begin{array}{l}
...@@ -261,12 +261,12 @@ _thus revolutionizing physics._ ...@@ -261,12 +261,12 @@ _thus revolutionizing physics._
**$`\begin{array}{l} **$`\begin{array}{l}
&nbsp; \\ &nbsp; \\
\mathbf{\displaystyle\quad\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}= -\dfrac{d}{dt}\iint_S\overrightarrow{B}\cdot\overrightarrow{dS}} \mathbf{\displaystyle\quad\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}= -\dfrac{d}{dt}\iint_S\overrightarrow{B}\cdot\overrightarrow{dS}}
\end{array}`$** \end{array}`$**
<br> <br>
* This equation plays an *important role in Neumann's induction phenomena*. * This equation plays an *important role in Neumann's induction phenomena*.
The quantity $`\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}`$ _The quantity $`\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}`$_
with the historically imperfect name "electromotive force (emf)", homogeneous to a voltage, is the origin of an electric current _with the historically imperfect name "electromotive force (emf)", homogeneous to a voltage, is the origin of an electric current_
flowing through the contour $`\Gamma`$ if it represents a conductive circuit. _flowing through the contour $`\Gamma`$ if it represents a conductive circuit._
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