The definition of magnetic momentum, as well as orbital and spin magnetic moment.
Also see the muon anomalous magnetic moment g-2.
The force on a loop of current due to a magnet:
Magnetic moment of a solenoid with current:
Orbital magnetic moment:
Magnetic moment of an electron:
Magnetic moment and spin of an electron:
Magnetic moment and spin of a positron:
Spin flip:
Edit and compile if you like:
% Author: Izaak Neutelings (March 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \dfrac
\usepackage{bm} % \bm
\usepackage{physics}
\usepackage{tikz,pgfplots}
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{patterns,snakes}
\tikzset{>=latex} % for LaTeX arrow head
\contourlength{1.6pt}
\usepackage{xcolor}
\colorlet{Bcol}{violet!90}
\colorlet{BFcol}{red!60!black}
\colorlet{Scol}{green!60!black}
\colorlet{veccol}{green!45!black}
\colorlet{Icol}{blue!70!black}
\colorlet{mucol}{red!90!black}
\tikzstyle{BField}=[->,thick,Bcol]
\tikzstyle{current}=[->,Icol] %thick,
\tikzstyle{force}=[->,thick,BFcol]
\tikzstyle{vector}=[->,thick,veccol]
\tikzstyle{mu vector}=[->,thick,mucol]
\tikzstyle{spin}=[->,very thick,Scol]
\tikzstyle{velocity}=[->,very thick,vcol]
\tikzstyle{charge+}=[very thin,draw=black,top color=red!50,bottom color=red!90!black,shading angle=20,circle,inner sep=0.5]
\tikzstyle{charge-}=[very thin,draw=black,top color=blue!50,bottom color=blue!80,shading angle=20,circle,inner sep=0.5]
\tikzstyle{metal}=[top color=black!15,bottom color=black!25,middle color=black!5,shading angle=10]
\tikzset{
BFieldLine/.style={thick,Bcol,decoration={markings,mark=at position #1 with {\arrow{latex}}},
postaction={decorate}},
BFieldLine/.default=0.5,
pics/magnet/.style={ %args={#1}
code={
\def\h{0.9}
\coordinate (-N) at (0,\h);
\coordinate (-S) at (0,-\h);
\draw[pic actions,thick,top color=red!60,bottom color=red!90,shading angle=20]
(-0.8*\h/2,0) rectangle ++(0.8*\h,\h);
\draw[pic actions,thick,top color=blue!60,bottom color=blue!90,shading angle=20]
(-0.8*\h/2,0) rectangle ++(0.8*\h,-\h);
\node[pic actions] at (0, \h/2) {\textbf{N}};
\node[pic actions] at (0,-\h/2) {\textbf{S}};
}},
}
\begin{document}
% B FIELD through current loop
\begin{tikzpicture}
\def\Rx{1.45}
\def\Ry{0.43}
\def\h{0.5}
\def\H{3}
\def\L{4}
\def\NB{5}
\def\ang{36}
\coordinate (O) at (0,0);
\coordinate (N) at (0,0.24*\H);
\coordinate (M) at (0,0.45*\H);
\coordinate (B) at (\ang:\H);
% MAGNETIC FIELD
\draw (-\Rx,0) arc (180:0:{\Rx} and {\Ry});
\begin{scope}
\clip ({-0.5*\L*cos(\ang)},-0.4*\H) rectangle ++({\L*cos(\ang)},\H);
%\foreach \i [evaluate={\y=(\i-0.5)*\H/(\NB-0.5)/2;
% \yl=-\H/2+(\i-0.5)*\H/(\NB-0.5)/2;}] in {1,...,\NB}{
% %\draw[BFieldLine,thin] (0,\y)++(\ang-180:0.5*\L) --++ (\ang:\L);
% %\draw[BFieldLine,thin] (0,-\y)++(\ang-180:0.5*\L) --++ (\ang:\L);
% \draw[BFieldLine,thin] (-\H/2,\y) -- ({-\H/2+(\H/2-\y)*cos(\ang)},\H/2);
% \draw[BFieldLine,thin] (-\H/2,-\y) -- ({-\H/2+(\H/2+\y)*cos(\ang)},+\H/2);
% \draw[BFieldLine,thin] ({\H/2-(\H/2+\yl)*cos(\ang)},-\H/2) -- (\H/2,\yl);
% \draw[BFieldLine,thin] ({\H/2-(\H/2-\yl)*cos(\ang)},-\H/2) -- (\H/2,-\yl);
%}
\foreach \i [evaluate={\x=-0.31*\H+(\i-1)*0.62*\H/(\NB-1);
\y=-cot(\ang)*\x;
\a=0.50+0.017*\i}] in {1,...,\NB}{ %0.58-0.02*(\i-\NB/2-1)^2
\draw[BFieldLine=\a] (\x,\y)++(\ang-180:\H) --++ (\ang:2*\H);
%\fill[red] (\x,\y) circle (0.05);
}
\end{scope}
\node[Bcol] at (\H/2,0.49*\H) {$\vb{B}$};
% CIRCUIT
\draw[white,very thick]
(-\Rx,0) arc (-180:0:{\Rx} and {\Ry});
\draw (-\Rx,0) arc (-180:0:{\Rx} and {\Ry});
%\draw[white,very thick] (0,0) ellipse ({\R} and {0.3*\R});
%\draw (0,0) ellipse ({\R} and {0.3*\R});
%\draw (0,0) ellipse ({\R} and {0.3*\R});
\draw[mu vector] (0,0) -- (M) node[above=-1] {$\vb*{\mu}$};
\draw[vector] (0,0) -- (N) node[midway,below=4,left=-1] {$\vu{n}$};
\draw pic[->,"\small$\;\theta$",draw=black,angle radius=14,angle eccentricity=1.4]
{angle = B--O--N};
\draw[white,very thick]
(-150:{1.1*\Rx} and {1.16*\Ry}) arc (-150:-80:{1.1*\Rx} and {1.16*\Ry});
\draw[current]
(-135:{1.1*\Rx} and {1.16*\Ry}) arc (-135:-90:{1.1*\Rx} and {1.16*\Ry})
node[midway,right=2,below] {$I$};
\end{tikzpicture}
% MAGNET FIELD through current loop - NS
\def\Rx{0.7}
\def\Ry{1.14}
\def\h{0.5}
\def\H{3}
\def\W{4}
\def\NB{2}
\begin{tikzpicture}
% MAGNETIC
\draw (0,\Ry) arc (90:270:{\Rx} and {\Ry});
\foreach \i [evaluate={\y=(0.34*\H)*\i^2/\NB; \in=1*\i^2; \out=180+10*\i^2; \f=0.26+0.10*\i;}] in {1,...,\NB}{
\draw[BFieldLine=\f] (0.25*\W, \y) to[out= \out,in= \in,looseness=0.8] (-0.95*\H, 0.4*\y/\H);
\draw[BFieldLine=\f] (0.25*\W,-\y) to[out=-\out,in=-\in,looseness=0.8] (-0.95*\H,-0.4*\y/\H);
}
\pic[rotate=90] (M) at (-0.9*\W,0) {magnet};
\node[Bcol] at (0.26*\W,0.52*\H) {$\vb{B}$};
% CIRCUIT
\draw[white,very thick]
(0,\Ry) arc (90:-90:{\Rx} and {\Ry});
\draw (0,\Ry) arc (90:-90:{\Rx} and {\Ry});
\draw[mu vector] (0,0) --++ (-0.3*\W,0) node[above left=-3] {\contour{white}{$\vb*{\mu}$}};
\draw[force] ( 95:{\Rx} and {\Ry}) --++ ( 140:0.7*\Ry) node[left=-1] {\contour{white}{$\vb{F}$}};
\draw[force] (-95:{\Rx} and {\Ry}) --++ (-140:0.7*\Ry) node[left=-1] {\contour{white}{$\vb{F}$}};
\draw[current]
(-70:{1.1*\Rx} and {1.1*\Ry}) arc (-70:-35:{1.1*\Rx} and {1.1*\Ry})
node[midway,right=2,below] {$I$};
\end{tikzpicture}
% MAGNET FIELD through current loop - SN
\begin{tikzpicture}
% MAGNETIC
\draw (0,\Ry) arc (90:270:{\Rx} and {\Ry});
\foreach \i [evaluate={\y=(0.34*\H)*\i^2/\NB; \out=1*\i^2; \in=180+10*\i^2; \f=0.80-0.10*\i;}] in {1,...,\NB}{
\draw[BFieldLine=\f] (-0.95*\H, 0.4*\y/\H) to[out= \out,in= \in,looseness=0.8] (0.25*\W, \y);
\draw[BFieldLine=\f] (-0.95*\H,-0.4*\y/\H) to[out=-\out,in=-\in,looseness=0.8] (0.25*\W,-\y);
}
\pic[rotate=-90] (M) at (-0.9*\W,0) {magnet};
\node[Bcol] at (0.26*\W,0.52*\H) {$\vb{B}$};
% CIRCUIT
\draw[force] ( 95:{\Rx} and {\Ry}) --++ (-25:0.8*\Ry) node[right=0] {\contour{white}{$\vb{F}$}};
\draw[force] (-95:{\Rx} and {\Ry}) --++ ( 25:0.8*\Ry) node[right=1] {\contour{white}{$\vb{F}$}};
\draw[white,very thick]
(0,\Ry) arc (90:-90:{\Rx} and {\Ry});
\draw (0,\Ry) arc (90:-90:{\Rx} and {\Ry});
\draw[mu vector] (0,0) --++ (-0.3*\W,0) node[above left=-3] {\contour{white}{$\vb*{\mu}$}};
\draw[current]
(-14:{1.1*\Rx} and {1.1*\Ry}) arc (-14:14:{1.1*\Rx} and {1.1*\Ry})
node[midway,right=2] {$I$};
\end{tikzpicture}
% SOLENOID
\begin{tikzpicture}[scale=1]
\def\A{9.0} % amplitude
\def\s{10} % coil segment length
\def\L{5.4} % coil length
\def\a{0.5} % coil segment aspect
\def\dy{1.0} % vertical shift
\def\dx{0.2} % horizontal shift
\draw[black!75,snake=coil,thick,segment amplitude=2*\A,segment length=\s,segment aspect=\a,very thick]
(-0.13*\L,0) -- (0,0) -- (\L,0) -- (1.08*\L,0);
\draw[-,thick]
(\L,0) -- (1.01*\L,0); % coil extension
\draw[current] (-0.12*\L,-0.015*\A) --++ (0.11*\L,0) node[midway,below] {$I$};
\draw[mu vector] (0.97*\L,-0.015*\A) --++ (0.18*\L,0) node[below] {$\vb*{\mu}$};
\end{tikzpicture}
% MAGNETIC MOMENT ATOM
\begin{tikzpicture}
\def\rn{0.3}
\def\re{0.15}
\def\Rx{1.5}
\def\Ry{0.5}
%\draw[dashed] (-100:1.5*\rn) -- (80:1.5*\rn);
\draw[dashed] (-\Rx,0) arc (180:0:{\Rx} and {\Ry});
\draw[mu vector] (0,-1.8*\rn) -- (0,2.9*\rn) node[right] {$\vb*{\mu}$};
\draw[charge+] (0,0) circle (\rn) node[scale=1.4] {+};
\draw[dashed] (\Rx,0) arc (0:-180:{\Rx} and {\Ry});
\draw[charge-]
(-40:{\Rx} and {\Ry}) circle (\re) node[scale=0.8] {$-$}
node[below right=4] {e};
\draw[->]
(-55:{1.15*\Rx} and {1.2*\Ry}) arc (-55:-72:{1.15*\Rx} and {1.2*\Ry});
\draw[current]
(-140:{1.15*\Rx} and {1.2*\Ry}) arc (-140:-100:{1.15*\Rx} and {1.2*\Ry})
node[midway,below] {$I$};
\end{tikzpicture}
% MAGNETIC MOMENT ELECTRON
\begin{tikzpicture}
\def\re{0.3}
\def\ang{80}
%\draw[dashed] (\ang-180:2.5*\re) -- (\ang:3.5*\re);
\draw[mu vector] (\ang-180:1.8*\re) -- (\ang:2.8*\re) node[right] {$\vb*{\mu}_\mathrm{e}$};
\draw[charge-]
(0,0) circle (\re) node[scale=1.4] {$-$}
node[right=10] {e};
\draw[->,rotate=\ang-90]
(0,-0.2*\re)++(-30:{1.6*\re} and {1.3*\re}) arc (-30:-165:{1.6*\re} and {1.3*\re})
--++ (110:0.3*\re);
\end{tikzpicture}
% MAGNETIC MOMENT ELECTRON + SPIN
\begin{tikzpicture}
\def\re{0.3}
\def\ang{80}
%\draw[dashed] (\ang-180:2.5*\re) -- (\ang:3.5*\re);
\draw[mu vector] (0,0) -- (\ang+180:3*\re) node[right] {$\vb*{\mu}_\mathrm{e}$};
\draw[spin] (0,0) -- (\ang:2.8*\re) node[right] {$\vb{S}$};
\draw[charge-]
(0,0) circle (\re) node[scale=1.4] {$-$}
node[right=10] {$\mathrm{e}^-$};
\draw[->,rotate=\ang-90]
(0,-0.2*\re)++(-175:{1.6*\re} and {1.3*\re}) arc (-175:-35:{1.6*\re} and {1.3*\re})
--++ (50:0.3*\re);
\end{tikzpicture}
% MAGNETIC MOMENT POSITRON + SPIN
\begin{tikzpicture}
\def\re{0.3}
\def\ang{80}
%\draw[dashed] (\ang-180:2.5*\re) -- (\ang:3.5*\re);
\draw[mu vector] (-0.28*\re,0) --++ (\ang:3*\re) node[below=3,left=0] {$\vb*{\mu}_\mathrm{e}$};
\draw[spin] (0.28*\re,0) --++ (\ang:2.8*\re) node[right] {$\vb{S}$};
\draw[charge+]
(0,0) circle (\re) node[scale=1.4] {$+$}
node[right=10] {$\mathrm{e}^+$};
\draw[->,rotate=\ang-90]
(0,-0.2*\re)++(-175:{1.6*\re} and {1.3*\re}) arc (-175:-35:{1.6*\re} and {1.3*\re})
--++ (50:0.3*\re);
\end{tikzpicture}
% MAGNETIC MOMENT FLIP
\begin{tikzpicture}
\def\rm{0.2}
\def\rx{1.9*\rm}
\def\ry{0.7*\rm}
\def\ang{80}
\def\W{1.7}
\def\H{2.8}
\coordinate (T) at (0,0.2*\H);
\coordinate (B) at (0,-0.2*\H);
% B FIELDS
\draw[BFieldLine] (-0.35*\W,-\H/2) --++ (0,\H);
\draw[BFieldLine] ( 0.65*\W,-\H/2) --++ (0,\H) node[right] {$\vb{B}$};
% VECTORS
\draw[mu vector] (T)++(\ang-180:1.3*\rm) --++ (\ang:3.6*\rm) node[right] {$\vb*{\mu}$}; %_\mathrm{e}
\draw[mu vector] (B)++(180-\ang:1.3*\rm) --++ (-\ang:3.6*\rm) node[right] {$\vb*{\mu}$};
\draw[<-,dashed,rotate=\ang-90]
(T)++(80:{\rx} and {\ry}) arc (80:-260:{\rx} and {\ry});
\draw[->,dashed,rotate=90-\ang]
(B)++(80:{\rx} and {\ry}) arc (80:-260:{\rx} and {\ry});
\draw[->]
(B)++(0.35*\W,0) arc (-50:50:0.36*\W);
\end{tikzpicture}
% LARMOR PRECESSION
\begin{tikzpicture}
\def\ang{55}
\def\S{1.0}
\def\B{1.4}
\def\Rx{\S*cos(\ang)}
\def\Ry{0.4*\Rx}
\coordinate (O) at (0,0);
\draw[BField] (O) -- (90:\B) node[left] {$\vb{B}$};
\draw[spin] (O) -- (\ang:\S) node[right] {$\vb{S}$};
\node[charge-,scale=1] (O) {$-$};
\draw[->,dashed]
(0,{\S*sin(\ang)})++(110:{\Rx} and {\Ry}) arc (110:440:{\Rx} and {\Ry})
node[right=3,above right=-2] {$\omega_\mathrm{S}$};
\end{tikzpicture}
\end{document}Click to download: magnetic_moment.tex • magnetic_moment.pdf
Open in Overleaf: magnetic_moment.tex
