From 32ecf3bb18ed84ba8d48c8802cb0c1dd54f76884 Mon Sep 17 00:00:00 2001
From: Florian Burgener <florian.brgnr@gmail.com>
Date: Fri, 15 Apr 2022 18:42:18 +0200
Subject: [PATCH] Update README

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+# Rapport sur la création d'une simulation de lignes de champ électrique
+
+Gawen Ackermann et Florian Burgener
+
+## Introduction
+
+Le but de ce travail est de créer une simulation permettant de visualiser le phénomène physique du champ électrique entre plusieurs atomes chargés. Plus précisément, ce travail permet d'observer le comportement des lignes de champ par rapport à des atomes chargés positivement ou négativement placé arbitrairement dans un univers discrétisé. Ci-dessous, vous pouvez observer l'application de la théorie du champ électrique entre deux charges, pour la partie de gauche les deux atomes sont chargés positivement et on la même charge et sur la partie de droite les atomes sont également de même charge, cependant le premier atome est chargé négativement tandis que le deuxième est chargé positivement.
+
+![](assets/introduction_electrical_field.png)
+
+<center>Figure 1 - Aperçu à ce que le résultat de la simulation devrait ressembler (si même setup)</center>
+
+Ce rapport se décompose en trois parties, la première partie est une explication de la théorie physique du champ électrique ainsi que des formules que nous avons utilisé pour créer cette simulation, la deuxième partie est une description détaillée de la façon dont nous avons appliqué la théorie, la dernière partie est une synthèse de ce travail ainsi qu'une réflexion sur les différentes possibilités d'améliorations que nous pourrions apporter à celui-ci.
+
+## Théorie
+
+### Formules de physique
+
+Un champ électrique est un champ qui entoure des particules chargées électriquement, il exerce une force sur toutes les autres particules chargées à intérieur de celui-ci ce qui a pour effet d'attirer ou de repousser les particules. La formule du champ électrique découle d'une transformation de la loi de Coulomb.
+
+Loi de Coulomb :
+$$
+\vec{F} = \frac{1}{4\pi\epsilon_0} \cdot \frac{\lvert q_0q_1 \rvert}{r^2}\hat{r} = K\frac{\lvert q_0q_1 \rvert}{r^2}\hat{r}
+$$
+où K est la constante de Coulomb $K = \frac{1}{4\pi\epsilon_0}$, $\epsilon_0$ étant la valeur de la permittivité du vide.
+
+Cette loi représente la force exercé entre deux particules chargées. La variable $r$ est la distance qui sépare le vecteur $\vec{x_0}$ du vecteur $\vec{x_1}$, $\vec{F}$ étant une grandeur vectorielle la direction de la force appliqué sur la particule 0 est le vecteur unitaire allant de $\vec{x_0}$ à $\vec{x_1}$ et qui est décrit par l'expression suivante $\hat{r} = \frac{\vec{x_1} - \vec{x_0}}{\lvert\lvert \vec{x_1} - \vec{x_0} \rvert\rvert}$ (multiplié par $-1$ si le signe de $q_1$ est le même que celui de $q_2$) et inversement pour la force appliqué sur la particule 1.
+
+Loi du champ électrique :
+$$
+\vec{E} = \frac{\vec{F}}{q_0} = K\frac{\lvert q_1 \rvert}{r^2}\hat{r}
+$$
+Il est important de noté que $q_0$ est toujours une charge positive ayant une charge beaucoup moins importante que $q_1$ 
+
+Avec cette formule, il est aisé observer que le champ électrique ne dépend que la charge $q_1$, le champ électrique résultant sera le champs électrique à la position de $q_0$. Le vecteur unitaire $\hat{r}$ est dans la direction de $q_0$ vers $q_1$ quand $q_1$ est une charge négative et dans la direction opposée quand $q_1$ est une charge positive.
+
+Principe de superposition du champ électrique :
+$$
+\vec{E} = \vec{E_1} + \vec{E_2} + \vec{E_3} + \cdots
+$$
+Le champ électrique en un point $p$ est la somme des champs électriques pour chacune des particules chargées au point $p$.
+
+### Description général de l'algorithme utilisé pour la simulation
+
+## Résultats
+
+## Conclusion
diff --git a/assets/introduction_electrical_field.png b/assets/introduction_electrical_field.png
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-- 
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