Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Champ magnétique créé par des courants électriques" situé à la page http://femto-physique.fr/electromagnetisme/biot_et_savart.php
% !TEX encoding = UTF-8 Unicode
% J.Roussel
% MAJ : 2014-06-03
% Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Champ magnétique créé par des courants électriques" situé à la page http://femto-physique.fr/electromagnetisme/biot_et_savart.php
%-------------------------------------------
\documentclass[11pt]{article}
\input{styles_emag}
\title{Figures TikZ du cours "Loi de Biot et Savart"}
\begin{document}
% 2016-01-10 : expérience d'oersted
\begin{tikzpicture}[scale=0.6]
\support{0.8}{0.2};
\draw[fill=black] (0,0)circle(3pt and 1pt);
\draw[line width=3pt] (0,0)--++(0,2);
\draw[fill=white,shift={(0,2)}](-120:5pt)--(60:5pt)--(-1.4,0)--cycle;
\draw[fill=red,shift={(0,2)}](60:5pt)--(-120:5pt)--(1.5,0)--cycle;
\draw[->,thin,shift={(0,2)}](1.6,0)to[bend left](1.35,-0.4);
\draw[thick,draw=white,double=black,double distance=2pt](-4,0.45)--(4,4.05);
\draw[draw=black,->](3,4)--++(-1.1,-.5)node[midway,above]{$I$};
\end{tikzpicture}
% 2016-01-09 : expérience d'ampère
\begin{tikzpicture}
\draw[shift={(-1,0)},rotate=20] (0,1) arc(100:440:0.4 and 1);
\draw[shift={(-1,0)},rotate=20,thick,decoration={markings,mark=at position 0.5cm with {\arrow[]{stealth};}},postaction=decorate] (0,1) arc(100:270:0.4 and 1);
\draw[shift={(-1,0)},rotate=20,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}},postaction=decorate](0,3)--++(0,-2);
\draw[shift={(-1,0)},rotate=20,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}},postaction=decorate](0,1)++(4pt,0)--++(0,2);
\draw[shift={(-1cm+2pt,0)},rotate=20,<->] (210:0.3 and .75) arc(210:150:0.3 and .75)--(-30:0.3 and .75)arc(-30:30:0.3 and .75);
\draw[->,shift={(-1,0)},rotate=20](2pt,0)node{$\bullet$}--++(1,0)node[right]{$\overrightarrow{n}$};
\draw[shift={(-1,0)},rotate=20](0,2)node[left=2pt]{$I$};
\draw[shift={(3,0)},rotate=-20] (0,1) arc(100:440:0.4 and 1);
\draw[shift={(3,0)},rotate=-20,thick,decoration={markings,mark=at position 0.5cm with {\arrow{stealth};}},postaction=decorate] (0,1) arc(100:270:0.4 and 1);
\draw[shift={(3,0)},rotate=-20,decoration={markings,mark=at position 1cm with {\arrow{stealth};}},postaction=decorate](0,3)--++(0,-2);
\draw[shift={(3,0)},rotate=-20,decoration={markings,mark=at position 1cm with {\arrow{stealth};}},postaction=decorate](0,1)++(4pt,0)--++(0,2);
\draw[shift={(3cm+2pt,0)},rotate=-20,<->] (210:0.3 and .75) arc(210:150:0.3 and .75)--(-30:0.3 and .75)arc(-30:30:0.3 and .75);
\draw[->,shift={(3,0)},rotate=-20](2pt,0)node{$\bullet$}--++(1,0)node[right]{$\overrightarrow{n}$};
\draw[shift={(3,0)},rotate=-20](0,2)node[left=2pt]{$I$};
\draw[force](0,-1)--++(1,0);
\draw[force](2.2,-1)--++(-1,0);
\end{tikzpicture}
% 2016-01-09 ; expérience de Rowland
\begin{tikzpicture}[scale=0.75]
\support{0.8}{0.2};
\draw[fill=black] (0,0)circle(3pt and 1pt);
\draw[line width=3pt] (0,0)--++(0,2);
\draw[fill=white,shift={(0,2)}](-120:5pt)--(60:5pt)--(-1.4,0)--cycle;
\draw[fill=red,shift={(0,2)}](60:5pt)--(-120:5pt)--(1.5,0)--cycle;
\draw[fill=gray] (-4,2cm-5pt)arc(270:90: 1.5pt and 5pt)--++(1,0)--++(0,-10pt)--cycle;
\draw[->,shift={(-4,2)}] (45:4.5pt and 15pt)arc(45:315:4.5pt and 15pt);
\draw[fill=gray] (-2.5,0) arc(270:90:0.6 and 2) --++(5pt,0)--++(0,-4)--++(-5pt,0);
\draw[fill=white] (-2.5cm+5pt,2) circle(0.6 and 2);
\draw[pattern=crosshatch] (-2.5cm+5pt,2) circle(0.6 and 2);
\node[coordinate,pin=right:{\footnotesize Disque chargé +}] at (-2,3.5) {};
\end{tikzpicture}
% 2016-01-05 : exemple du fil infini
\begin{tikzpicture}[scale=0.8,x={(-0.353cm,-0.353cm)}, y={(1cm,0cm)}, z={(0cm,1cm)},decoration={markings,mark=at position 1.5cm with {\arrow[]{stealth};}}]
\coordinate (O) at (0, 0, 0);
\coordinate (P) at (0,0,2);
\coordinate (M) at ({3* cos(60)}, {3*sin(60)},0);
\coordinate (A) at ({2* cos(60)}, {2*sin(60)},0);
\draw[axis] (O) -- +(0,0,4)node[above]{$z$};
\draw[axis] (O) -- +(4,0,0) ;
\draw[axis] (O) -- +(0,4,0) ;
\draw[dotted] (O) circle(3);
\draw[force](M)--++({-2.5*sin(60)}, {2.5*cos(60)},0)node[above]{$\overrightarrow{\mathrm{d}B}$};
\draw[vecteur](M)--($1.5*(M)$)node[right]{$\overrightarrow{u_r}$};
\draw[vecteur](M)--++({-sin(60)}, {cos(60)},0)node[above left]{$\overrightarrow{u_\theta}$};
\draw[ultra thick,gray,postaction=decorate](0,0,-3)--++(0,0,6.9)node[pos=0.25,left]{$I$};
\draw[dashed] (P)--(M)node[below]{M};
\draw[ultra thick,<-] (P)node[left]{\footnotesize P}++(0,0,.2)--++(0,0,-.4);
\draw[<-](P)++(0,.1,0) to[bend right] (0,0.5,2.5)node[above right=-1pt]{\footnotesize $\overrightarrow{\mathrm{d}\ell}$};
\draw[dashed] (O)--(M) node{$\bullet$} node[midway,below=1pt]{$r$};
\draw[draw=white,double=black] (0.15,0.26,0)--++(0,0,0.2)--(0,0,0.2);
\draw (A) to[bend left]($0.3*(P)+0.7*(M)$);
\draw (A) node[above left=2pt,fill=white]{$\varphi$};
\draw[vecteur](P)--($0.3*(M)+0.7*(P)$)node[pos=0.7,right]{$\overrightarrow{u}$};
\end{tikzpicture}
% 2016-01-05 : ligne de champ d'un fil infini
\begin{tikzpicture}[x={(-0.353cm,-0.353cm)}, y={(1cm,0cm)}, z={(0cm,1cm)},decoration={markings,mark=at position 1.5cm with {\arrow[red]{stealth};}}]
\coordinate (O) at (0, 0, 0);
\coordinate (M) at ({cos(60)}, {sin(60)},0);
\draw[ultra thick,red,](0,0,-2)--++(0,0,2);
%draw a grid in the x-y plane
\draw[black,fill=green!25,opacity=0.75](2.5,-2.5,0)--++(0,5,0)--++(-5,0,0)--+(0,-5,0)--cycle;
\foreach \x in {-2.5,-2,...,2.5}
\foreach \y in {-2.5,-2,...,2.5}
{
\draw[very thin,lightgray,opacity=0.5] (\x,-2.5,0) -- (\x,2.5,0);
\draw[very thin,lightgray,opacity=0.5] (-2.5,\y,0) -- (2.5,\y,0);
}
\draw[thick,postaction=decorate,decoration={markings,mark=at position 1.5cm with {\arrow{stealth};}}] (O) circle(1);
\draw[thick,postaction=decorate,decoration={markings,mark=at position 1.5cm with {\arrow{stealth};}}] (O) circle(1.5);
\draw[thick,postaction=decorate,decoration={markings,mark=at position 1.5cm with {\arrow{stealth};}}] (O) circle(2);
\tirebouchon{shift={(0,1,2)},scale=0.6};
\draw[postaction=decorate,draw=white,double=red,double distance=1.5pt](0,0,0)--++(0,0,3)node[pos=0.6,left]{$I$};
\end{tikzpicture}
% 2016-01-06 : symétries du champ magnétique
\begin{tikzpicture}
\draw (0,3) node{$\overrightarrow{B}=\overrightarrow{u}\wedge \overrightarrow{v}$};
\draw[->] (2,1)--++(-60:1.4)node[below]{$\overrightarrow{v}$};
\draw[->] (2,1)--++(-110:0.8)node[below]{$\overrightarrow{u}$};
\draw[shift={(2,1)},rotate=-60] circle(1 and 0.3);
\draw[shift={(2,1)},rotate=-60,thick,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}},postaction=decorate] (-1,0) arc(-180:0:1 and 0.3);
\draw[force] (2,1)node{$\bullet$}--++(30:1.6)node[right]{$\overrightarrow{B}$};
\draw[->] (-2,1)--++(-120:1.4)node[below]{$\overrightarrow{v'}$};
\draw[force] (-2,1)node{$\bullet$}--++(-30:1.6)node[right]{$\overrightarrow{B'}$};
\draw[shift={(-2,1)},rotate=60] circle(1 and 0.3);
\draw[draw=white,double=black,shift={(-2,1)},rotate=60,decoration={markings,mark=at position 1.5cm with {\arrowreversed[black]{stealth};}},postaction=decorate] (-1,0) arc(-180:0:1 and 0.3);
\draw[->] (-2,1)--++(-70:0.8)node[below]{$\overrightarrow{u'}$};
\node[coordinate,pin=below right:{\footnotesize Plan de symétrie}] at (0.1,-1) {};
\draw[dashed](0,-1.5)--++(0,4);
\draw[force] (0,-.5) node(M)[monBleu]{•}--++(1,0);
\end{tikzpicture}
% 2016-01-06 : anti-symétries du champ magnétique
\begin{tikzpicture}
\draw (0,3) node{$\overrightarrow{B}=\overrightarrow{u}\wedge \overrightarrow{v}$};
\draw[->] (2,1)--++(-60:1.4)node[below]{$\overrightarrow{v}$};
\draw[->] (2,1)--++(-110:0.8)node[below]{$\overrightarrow{u}$};
\draw[force] (2,1)node{$\bullet$}--++(30:1.6)node[right]{$\overrightarrow{B}$};
\draw[shift={(2,1)},rotate=-60] circle(1 and 0.3);
\draw[shift={(2,1)},rotate=-60,thick,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}},postaction=decorate] (-1,0) arc(-180:0:1 and 0.3);
\draw[->] (-2,1)--++(60:1.4)node[above]{$\overrightarrow{v'}$};
\draw[->] (-2,1)--++(110:0.8)node[above]{$\overrightarrow{u'}$};
\draw[force] (-2,1)node{$\bullet$}--++(150:1.6)node[left]{$\overrightarrow{B'}$};
\draw[shift={(-2,1)},rotate=60] circle(1 and 0.3);
\draw[shift={(-2,1)},rotate=60,thick,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}},postaction=decorate] (-1,0) arc(-180:0:1 and 0.3);
\node[coordinate,pin=below right:{\footnotesize Plan d'anti-symétrie}] at (0.1,-1) {};
\draw[dashed](0,-1.5)--++(0,4);
\draw[force] (0,-0.5) node(M)[monBleu]{•}--++(0,1);
\end{tikzpicture}
% 2016-01-11 : plans de symétrie d'un solénoide
\begin{tikzpicture}[decoration={markings,mark=at position 1.5cm with {\arrow[red]{stealth};}}]
\draw[thick,red,postaction=decorate](-1,0,-1) arc(180:360:1);
\draw[thick,red,postaction=decorate](-1,0,-.5) arc(180:360:1);
\draw[thick,red,postaction=decorate](-1,0,0) arc(180:360:1);
\draw[thick,red,postaction=decorate](-1,0,.5) arc(180:360:1);
\draw[thick,red,postaction=decorate](-1,0,1) arc(180:360:1);
\draw[black,fill=green!25,opacity=0.75](-2.5,0,2.5)--++(5,0,0)--++(0,0,-5)--+(-5,0,0)--cycle;
\draw[thick,red](0,1,-1) arc(90:180:1);
\draw[thick,red](0,1,-.5) arc(90:180:1);
\draw[thick,red](0,1,0) arc(90:180:1);
\draw[thick,red](0,1,.5) arc(90:180:1);
\draw[thick,red](0,1,1) arc(90:180:1);
\draw[black,fill=green!25,opacity=0.75](0,2.5,2.5)--++(0,-2.5,0)--++(0,0,-5)--+(0,2.5,0)--cycle;
\draw[thick,red,postaction=decorate](1,0,-1) arc(0:90:1);
\draw[thick,red,postaction=decorate](1,0,-.5) arc(0:90:1);
\draw[black,fill=green!25,opacity=0.75](0,0,0)--++(0,2.5,0)--++(2.5,0,0)--++(0,-2.5,0)--cycle;
\draw[thick,red,postaction=decorate](1,0,0) arc(0:90:1);
\draw[thick,red,postaction=decorate](1,0,.5) arc(0:90:1);
\draw[thick,red,postaction=decorate](1,0,1) arc(0:90:1);
\node[coordinate,pin=right:{\footnotesize Plan d'anti-symétrie}] at (0,2,-2.5) {};
\node[coordinate,pin=right:{\footnotesize Plan de symétrie}] at (2.5,2,0) {};
\node[coordinate,pin=right:{\footnotesize Plan d'anti-symétrie}] at (2.5,0,2) {};
\end{tikzpicture}
% 2016-01-07 : champ créé par une spire
\begin{tikzpicture}[scale=1]
\coordinate (M) at (0,3);
\coordinate (P) at (-150:2 and 0.6);
\coordinate (N) at (0,{3+sin(atan(2/3))});
\coordinate (Q) at (-150:1 and 0.3);
\draw[gray](0,0)--++(0,3.5);
\draw[force] (M)--(N)node[right]{\footnotesize $\overrightarrow{\mathrm{d}B_z}$};
\draw[densely dotted] (N) circle(1 and 0.3);
\draw[densely dotted](N)--($(N)+(Q)$);
\draw[gray,->](0,3.5)--++(0,1)node[right]{$z$};
\draw[axis](P)--(0,0)node[pos=0.7,fill=white]{\footnotesize $R$};
\draw (0,0) circle(2 and 0.6);
\draw[->] (P) arc(-150:-135:2 and 0.6);
\draw[thick,decoration={markings,mark=at position 2.5cm with {\arrow[]{stealth};}},postaction=decorate] (-2,0) arc(-180:0:2 and 0.6);
\draw (P)node[below=3pt]{\footnotesize $\overrightarrow{\mathrm{d}\ell}$}++(0,-2pt)--++(0,4pt)node[above]{\footnotesize P}++(0,-2pt)--(M)node[midway,left]{\footnotesize $r$}node[right]{\footnotesize M};
\draw[->] (P)--++($0.3*(M)-0.3*(P)$)node[midway,right]{$\overrightarrow{u}$};
\draw[force](M)--($(N)+(Q)$)node[below=5pt]{\footnotesize$\overrightarrow{\mathrm{d}B}$};
\draw (M)++(0,-.5) arc(-90:-118:0.5);
\draw (M)++(-105:0.5)node[below]{$\theta$};
\draw[rotate=-28](M)++(-5pt,0)--++(0,-5pt)--++(5pt,0);
\draw (0,-0.6)node[below]{$I$};
\end{tikzpicture}
% 2016-01-10 : dipole magnétique
\begin{tikzpicture}[decoration={markings,mark=at position 1.5cm with {\arrow[monBleu]{stealth};}}]
\clip circle(3);
\foreach \K in{1.5,2.9,6,12}{
\draw [postaction=decorate,thin, color=monBleu, domain=pi/2:-pi/2, samples=50]plot (xy polar cs:angle=\x r, radius={\K*cos(\x r)*cos(\x r)});
\draw [postaction=decorate,thin, color=monBleu, domain=pi/2:3*pi/2,samples=50]plot (xy polar cs:angle=\x r, radius={\K*cos(\x r)*cos(\x r)});
}
\draw[postaction=decorate,thin,color=monBleu](0,0)--(0,3);
\draw[postaction=decorate,thin,color=monBleu](0,-3)--(0,3);
\draw[dashed,fill=white]circle(0.5);
\draw[->] (0,-5pt)--++(0,10pt)node[midway,right]{\footnotesize $\overrightarrow{m}$};
\end{tikzpicture}
% 2016-01-10 : géomagnétisme
\begin{tikzpicture}[]
\node[coordinate,pin=above right:{\scriptsize Nord géographique}] at (0,2.35) {};
\node[coordinate,pin=below left:{\scriptsize Sud géographique}] at (0,-2.35) {};
\draw (0,3.3) arc(90:101.5:3.3);
\draw (95:3.3)node[above]{\scriptsize 11,5°};
\clip circle(3.5);
\draw[very thin,gray](0,3.5)--(0,-3.5);
\node[inner sep=0] at (0,0) {\includegraphics[width=5cm]{earth.png}};
\foreach \K/\Q in{2.5/.3,5/.8,10/1.1,20/1.3}{
\draw [rotate=11.5,>-<,thin, color=monBleu, domain=\Q:{pi-\Q}, samples=50, smooth]plot (xy polar cs:angle=\x r, radius={\K*cos(\x r)*cos(\x r)});
\draw [rotate=11.5,thin, color=monBleu, domain={pi-\Q}:{2*pi+\Q}, samples=50, smooth]plot (xy polar cs:angle=\x r, radius={\K*cos(\x r)*cos(\x r)});
}
\draw[rotate=11.5,thin,color=monBleu](0,3.5)--(0,1);
\draw[rotate=11.5,thin,color=monBleu,>->](0,1)--(0,-2);
\draw[rotate=11.5,thin,color=monBleu](0,-2)--(0,-3.5);
\aimant{scale=0.7,rotate=-78.5,shift={(-1,0)}};
\fill (0,2.35)circle(3pt and 1pt);
\fill (0,-2.35)circle(3pt and 1pt);
\fill[rotate=11.5,shift={(2.5,0)},red](-2pt,0)--(2pt,0)--(0,8pt)node[above,color=gray]{\scriptsize N}--cycle;
\fill[rotate=11.5,shift={(2.5,0)}](-2pt,0)--(2pt,0)--(0,-8pt)node[below,color=gray]{\scriptsize S}--cycle;
\end{tikzpicture}
% origine du magnétisme des aimants
\begin{tikzpicture}
%phase paramagnétique
\draw (0,0) rectangle(5,2);
\foreach \x in {.5,1,1.5,2,2.5,3,3.5,4,4.5}
\foreach \y in {.4,1,1.6}{
\pgfmathrandominteger{\a}{0}{360}
\boucle{shift={(\x,\y)},scale=.75,rotate=\a};
}
%pahse ferromagnétique
\draw[shift={(0,-2.5)}] (0,0) rectangle(5,2);
\draw[shift={(0,-2.5)}] (0,1)node[left]{S}++(5,0)node[right]{N};
\foreach \x in {.5,1,1.5,2,2.5,3,3.5,4,4.5}
\foreach \y in {.4,1,1.6}{
\pgfmathrandominteger{\a}{-10}{10}
\boucle{shift={(\x,{\y-2.5})},scale=.75,rotate=\a};
}
%expérience de l'aiamnt brisée
\draw[shift={(0,-5)}] (0,0)--++(0,2)--++(2.2,0) decorate[decoration=saw]{--(2.2,0)}-- cycle;
\draw[shift={(0,-5)}] (2.8,0) decorate[decoration=saw]{--(2.8,2)}--++(2.2,0)--++(0,-2)-- cycle;
\foreach \x in {.3,0.8,1.3,1.8,3,3.5,4,4.5}
\foreach \y in {.4,1,1.6}{
\pgfmathrandominteger{\a}{-10}{10}
\boucle{shift={(\x,{\y-5})},scale=.75,rotate=\a};
}
\draw[shift={(0,-5)}] (0,1)node[left]{S}++(2.5,0)node[fill=white,left]{N}node[fill=white,right]{S}++(2.5,0)node[right]{N};
\end{tikzpicture}
\end{document}