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Field lines in a parallel plate capacitor with border effect
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4
I am drawing qualitatively the field lines bending near the edges of a parallel plate capacitor with tikz. The code is:
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrary positioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
begin tikzpicture[thick, scale=0.9, every node/.style=transform
shape, decoration=
markings, mark=at position 0.5 with arrowlatex]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
The image I get is this:
I would like to improve the alignment of the arrow tips on the curved lines.
The arrow bases are off the lines. They should be aligned more symmetrically.
How could I fix/improve this? Perhaps just changing the arrow types will do it. The stealth style improves, but still a bit off.
Thanks in advance!
tikz-pgf
asked May 2 at 13:44
minmaxminmax
1233
add a comment |
4
I am drawing qualitatively the field lines bending near the edges of a parallel plate capacitor with tikz. The code is:
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrary positioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
begin tikzpicture[thick, scale=0.9, every node/.style=transform
shape, decoration=
markings, mark=at position 0.5 with arrowlatex]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
The image I get is this:
I would like to improve the alignment of the arrow tips on the curved lines.
The arrow bases are off the lines. They should be aligned more symmetrically.
How could I fix/improve this? Perhaps just changing the arrow types will do it. The stealth style improves, but still a bit off.
Thanks in advance!
tikz-pgf
asked May 2 at 13:44
minmaxminmax
1233
I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13
add a comment |
4
4
4
0
I am drawing qualitatively the field lines bending near the edges of a parallel plate capacitor with tikz. The code is:
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrary positioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
begin tikzpicture[thick, scale=0.9, every node/.style=transform
shape, decoration=
markings, mark=at position 0.5 with arrowlatex]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
The image I get is this:
I would like to improve the alignment of the arrow tips on the curved lines.
The arrow bases are off the lines. They should be aligned more symmetrically.
How could I fix/improve this? Perhaps just changing the arrow types will do it. The stealth style improves, but still a bit off.
Thanks in advance!
tikz-pgf
asked May 2 at 13:44
minmaxminmax
1233
I am drawing qualitatively the field lines bending near the edges of a parallel plate capacitor with tikz. The code is:
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrary positioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
begin tikzpicture[thick, scale=0.9, every node/.style=transform
shape, decoration=
markings, mark=at position 0.5 with arrowlatex]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
The image I get is this:
I would like to improve the alignment of the arrow tips on the curved lines.
The arrow bases are off the lines. They should be aligned more symmetrically.
How could I fix/improve this? Perhaps just changing the arrow types will do it. The stealth style improves, but still a bit off.
Thanks in advance!
tikz-pgf
tikz-pgf
asked May 2 at 13:44
minmaxminmax
1233
asked May 2 at 13:44
minmaxminmax
1233
asked May 2 at 13:44
minmaxminmax
1233
asked May 2 at 13:44
minmaxminmax
1233
asked May 2 at 13:44
minmaxminmax
1233
1233
I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13
add a comment |
I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13
I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13
add a comment |
1 Answer
1
active
oldest
votes
6
Welcome to TeX-SE! The issue is that you attach a straight arrow to a curved line. So the first step is to bend the arrow. But then the decorations do not know a priori the curvature at a given point, which can be fixed by recording some coordinates along the path and then draw a curved arrow through these coordinates.
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrarypositioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows.meta,bending
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
% from https://tex.stackexchange.com/a/430239/121799
tikzset% inspired by https://tex.stackexchange.com/a/316050/121799
arc arrow/.style args=%
to pos #1 with length #2
decoration=
markings,
mark=at position 0 with pgfextra%
pgfmathsetmacrotmpArrowTime#2/(pgfdecoratedpathlength)
xdeftmpArrowTimetmpArrowTime,
mark=at position #1-tmpArrowTime with coordinate(@1);,
mark=at position #1-2*tmpArrowTime/3 with coordinate(@2);,
mark=at position #1-tmpArrowTime/3 with coordinate(@3);,
mark=at position #1 with coordinate(@4);
draw[-Latex[length=#2,bend]]
(@1) .. controls (@2) and (@3) .. (@4);,
,
begintikzpicture[thick, scale=0.9, every node/.style=transform
shape, arc arrow=to pos 0.525 with length 2mm]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
answered May 2 at 15:36
marmotmarmot
126k6162308
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
add a comment |
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votes
6
Welcome to TeX-SE! The issue is that you attach a straight arrow to a curved line. So the first step is to bend the arrow. But then the decorations do not know a priori the curvature at a given point, which can be fixed by recording some coordinates along the path and then draw a curved arrow through these coordinates.
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrarypositioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows.meta,bending
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
% from https://tex.stackexchange.com/a/430239/121799
tikzset% inspired by https://tex.stackexchange.com/a/316050/121799
arc arrow/.style args=%
to pos #1 with length #2
decoration=
markings,
mark=at position 0 with pgfextra%
pgfmathsetmacrotmpArrowTime#2/(pgfdecoratedpathlength)
xdeftmpArrowTimetmpArrowTime,
mark=at position #1-tmpArrowTime with coordinate(@1);,
mark=at position #1-2*tmpArrowTime/3 with coordinate(@2);,
mark=at position #1-tmpArrowTime/3 with coordinate(@3);,
mark=at position #1 with coordinate(@4);
draw[-Latex[length=#2,bend]]
(@1) .. controls (@2) and (@3) .. (@4);,
,
begintikzpicture[thick, scale=0.9, every node/.style=transform
shape, arc arrow=to pos 0.525 with length 2mm]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
answered May 2 at 15:36
marmotmarmot
126k6162308
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
add a comment |
6
Welcome to TeX-SE! The issue is that you attach a straight arrow to a curved line. So the first step is to bend the arrow. But then the decorations do not know a priori the curvature at a given point, which can be fixed by recording some coordinates along the path and then draw a curved arrow through these coordinates.
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrarypositioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows.meta,bending
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
% from https://tex.stackexchange.com/a/430239/121799
tikzset% inspired by https://tex.stackexchange.com/a/316050/121799
arc arrow/.style args=%
to pos #1 with length #2
decoration=
markings,
mark=at position 0 with pgfextra%
pgfmathsetmacrotmpArrowTime#2/(pgfdecoratedpathlength)
xdeftmpArrowTimetmpArrowTime,
mark=at position #1-tmpArrowTime with coordinate(@1);,
mark=at position #1-2*tmpArrowTime/3 with coordinate(@2);,
mark=at position #1-tmpArrowTime/3 with coordinate(@3);,
mark=at position #1 with coordinate(@4);
draw[-Latex[length=#2,bend]]
(@1) .. controls (@2) and (@3) .. (@4);,
,
begintikzpicture[thick, scale=0.9, every node/.style=transform
shape, arc arrow=to pos 0.525 with length 2mm]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
answered May 2 at 15:36
marmotmarmot
126k6162308
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
add a comment |
6
6
6
Welcome to TeX-SE! The issue is that you attach a straight arrow to a curved line. So the first step is to bend the arrow. But then the decorations do not know a priori the curvature at a given point, which can be fixed by recording some coordinates along the path and then draw a curved arrow through these coordinates.
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrarypositioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows.meta,bending
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
% from https://tex.stackexchange.com/a/430239/121799
tikzset% inspired by https://tex.stackexchange.com/a/316050/121799
arc arrow/.style args=%
to pos #1 with length #2
decoration=
markings,
mark=at position 0 with pgfextra%
pgfmathsetmacrotmpArrowTime#2/(pgfdecoratedpathlength)
xdeftmpArrowTimetmpArrowTime,
mark=at position #1-tmpArrowTime with coordinate(@1);,
mark=at position #1-2*tmpArrowTime/3 with coordinate(@2);,
mark=at position #1-tmpArrowTime/3 with coordinate(@3);,
mark=at position #1 with coordinate(@4);
draw[-Latex[length=#2,bend]]
(@1) .. controls (@2) and (@3) .. (@4);,
,
begintikzpicture[thick, scale=0.9, every node/.style=transform
shape, arc arrow=to pos 0.525 with length 2mm]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
answered May 2 at 15:36
marmotmarmot
126k6162308
Welcome to TeX-SE! The issue is that you attach a straight arrow to a curved line. So the first step is to bend the arrow. But then the decorations do not know a priori the curvature at a given point, which can be fixed by recording some coordinates along the path and then draw a curved arrow through these coordinates.
documentclass[margin=10pt]standalone
usepackagetikz
usepackagebm
%usepackagepgfmath
usetikzlibrarypositioning
usetikzlibrarycalc,fadings,decorations.pathreplacing, arrows.meta,bending
usetikzlibrarydecorations.pathmorphing,patterns
usetikzlibrarydecorations.markings
begindocument
% from https://tex.stackexchange.com/a/430239/121799
tikzset% inspired by https://tex.stackexchange.com/a/316050/121799
arc arrow/.style args=%
to pos #1 with length #2
decoration=
markings,
mark=at position 0 with pgfextra%
pgfmathsetmacrotmpArrowTime#2/(pgfdecoratedpathlength)
xdeftmpArrowTimetmpArrowTime,
mark=at position #1-tmpArrowTime with coordinate(@1);,
mark=at position #1-2*tmpArrowTime/3 with coordinate(@2);,
mark=at position #1-tmpArrowTime/3 with coordinate(@3);,
mark=at position #1 with coordinate(@4);
draw[-Latex[length=#2,bend]]
(@1) .. controls (@2) and (@3) .. (@4);,
,
begintikzpicture[thick, scale=0.9, every node/.style=transform
shape, arc arrow=to pos 0.525 with length 2mm]
defLx5.0
defxi0.25
defdx0.5
defdy0.35
defhh2.0
% top plate
filldraw[opacity=0.2] (0, 0) -- (Lx, 0) -- (Lx, dy) -- (0, dy);
draw (Lx/2, hh+2.*dy) node[] $bm -Q$;
% bottom plate
filldraw[opacity=0.2] (0, hh) -- (Lx, hh) -- (Lx, hh+dy) -- (0, hh+dy);
draw (Lx/2, -dy) node[] $bm +Q$;
% left curved lines
draw[postaction=decorate] (xi, dy) node[below= -0.14, red] $bm +$ to
[bend left=15] (xi, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (0, dy) .. controls (-dx, 0.35*(hh+dy)) and (-dx,0.65*(hh+dy)) .. (0, hh);
draw[postaction=decorate] (0, 0.7*dy) .. controls (-3*dx, 0.1*(hh+dy))
and (-3*dx,0.9*(hh+dy)) .. (0, hh+0.3*dy);
draw[postaction=decorate] (0, 0.2*dy) .. controls (-6*dx, 0.0*(hh+dy))
and (-6*dx,(hh+dy)) .. (0, hh+0.8*dy);
% Middle lines
foreach nL in 1, 2, ..., 8
draw[red] (xi+nL*dx, 0.65*dy) node[] $bm +$;
draw[blue] (xi+nL*dx, hh+0.1*dy) node[] $bm -$;
draw[postaction=decorate] (xi+nL*dx, dy) --++ (0, hh-dy);
% right curved lines
draw[postaction=decorate] (xi+9*dx, dy) node[below= -0.14, red] $bm +$
to [bend right=15] (xi+9*dx, hh) node[above=-0.24, blue] $bm -$;
draw[postaction=decorate] (Lx, dy) .. controls (Lx+dx, 0.35*(hh+dy)) and (Lx+dx,0.65*(hh+dy)) .. (Lx, hh);
draw[postaction=decorate] (Lx, 0.7*dy) .. controls (Lx+3*dx,
0.1*(hh+dy)) and (Lx+3*dx,0.90*(hh+dy)) .. (Lx, hh+0.3*dy);
draw[postaction=decorate] (Lx, 0.2*dy) .. controls (Lx+6*dx,
0.0*(hh+dy)) and (Lx+6*dx,(hh+dy)) .. (Lx, hh+0.8*dy);
endtikzpicture
enddocument
answered May 2 at 15:36
marmotmarmot
126k6162308
answered May 2 at 15:36
marmotmarmot
126k6162308
answered May 2 at 15:36
marmotmarmot
126k6162308
answered May 2 at 15:36
marmotmarmot
126k6162308
126k6162308
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
add a comment |
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
1
1
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
Worked very well. Very nice piece of tikz witchcraft! Thanks!
– minmax
May 2 at 19:58
add a comment |
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I've been puttng a lot of thought into computing field lines. First, field lines are the gradient of the potential (scalar) field. Second, conductors form equipotential volumes. The charge distribution is not even, but will migrate until all the potentials even out. Consequently, the equipotential lines are parallel between the plates all the way to the edge.
– John Kormylo
May 2 at 21:01
This is just qualitative. I didn't mean to be accurate. It's just to show that there will be field lines outside the parallel plates. If the problem is 2d, one can use conformal mapping. See here: demonstrations.wolfram.com/…. Actually, only the middle equipotential will be truly planar.
– minmax
May 8 at 17:31
And the interiors of the conductors. A thicker conductor (I suspect the linked example was infinitely thin) would produce a different result. I just couldn't imagine a field that could be constant over such a large volume without being constant in between.
– John Kormylo
May 8 at 22:13