File:Charge and dielectric.gif
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Charge_and_dielectric.gif (480 × 536 pixels, file size: 3.63 MB, MIME type: image/gif, looped, 102 frames, 10 s)
Captions
Captions
Field generated by a charge next to a dielectric.
Summary[edit]
| Description |
English: A point charge next to a planar interface with a dielectric will create an electric field that depends both on its position, and the dielectric constant (the higher the dielectric constant, the weaker the field inside). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1315975665385123842 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.1 code[edit]
d =.
\[CurlyPhi]l[d_, x_, y_] := 1/(4 \[Pi] \[Epsilon]0 \[Epsilon]r) ((((2 \[Epsilon]r)/(\[Epsilon]r + 1)) q)/Sqrt[(x - d)^2 + y^2]);
\[CurlyPhi]r[d_, x_, y_] := 1/(4 \[Pi] \[Epsilon]0) (q/Sqrt[(x - d)^2 + y^2] - (((\[Epsilon]r - 1)/(\[Epsilon]r + 1)) q)/Sqrt[(x + d)^2 + y^2]);
\[Epsilon]0 = 1; \[Epsilon]r = 2; q = 1; d = (7/4) Cos[2 \[Pi] t + ArcCos[-1/7]] + 9/4;
er[d_, x_, y_] := Evaluate[-Grad[\[CurlyPhi]r[d, x, y], {x, y}]];
el[d_, x_, y_] := Evaluate[-Grad[\[CurlyPhi]l[d, x, y], {x, y}] ];
e = Piecewise[{{el[d, x, y], x < 0}, {er[d, x, y], x > 0}}];
p0 = Table[
Show[
VectorPlot[e, {x, -5, 5}, {y, -5, 5}, Background -> Black, Frame -> False]
,
LabelStyle -> {White, Bold, FontSize -> 20}, PlotRange -> All, Epilog -> {White, Thick, Line[{{0, -6}, {0, 6}}],
Disk[{d, 0}, 0.2], Text[Style[StringForm["\!\(\*SubscriptBox[\(\[Epsilon]\), \(r\)]\)=``", NumberForm[\[Epsilon]r, {3, 2}]], White, Bold, FontSize -> 22], {-3., 5.3}],
Text[Style["\!\(\*SubscriptBox[\(\[Epsilon]\), \(r\)]\)=1", White, Bold, FontSize -> 22], {3., 5.3}]}, Frame -> False, PlotLabel -> "\!\(\*OverscriptBox[\(E\), \(\[Rule]\)]\)"
]
, {t, 0, 1, 0.02}];
\[Epsilon]r =.
\[CurlyPhi]l[d_, x_, y_] := 1/(4 \[Pi] \[Epsilon]0 \[Epsilon]r) ((((2 \[Epsilon]r)/(\[Epsilon]r + 1)) q)/Sqrt[(x - d)^2 + y^2]);
\[CurlyPhi]r[d_, x_, y_] := 1/(4 \[Pi] \[Epsilon]0) (q/Sqrt[(x - d)^2 + y^2] - (((\[Epsilon]r - 1)/(\[Epsilon]r + 1)) q)/Sqrt[(x + d)^2 + y^2]);
\[Epsilon]0 = 1; \[Epsilon]r = ((12 - 1)/2) Cos[2 \[Pi] t + ArcCos[-9/11]] + (12 + 1)/2; q = 1; d = 2;
er[d_, x_, y_] := Evaluate[-Grad[\[CurlyPhi]r[d, x, y], {x, y}]];
el[d_, x_, y_] := Evaluate[-Grad[\[CurlyPhi]l[d, x, y], {x, y}] ];
e = Piecewise[{{el[d, x, y], x < 0}, {er[d, x, y], x > 0}}];
p1 = Table[
Show[
VectorPlot[e, {x, -5, 5}, {y, -5, 5}, Background -> Black, Frame -> False]
,
LabelStyle -> {White, Bold, FontSize -> 20}, PlotRange -> All, Epilog -> {White, Thick, Line[{{0, -6}, {0, 6}}],
Disk[{d, 0}, 0.2], Text[Style[StringForm["\!\(\*SubscriptBox[\(\[Epsilon]\), \(r\)]\)=``", NumberForm[\[Epsilon]r, {3, 2}]], White, Bold, FontSize -> 22], {-3., 5.3}],
Text[Style["\!\(\*SubscriptBox[\(\[Epsilon]\), \(r\)]\)=1", White, Bold, FontSize -> 22], {3., 5.3}]}, Frame -> False, PlotLabel -> "\!\(\*OverscriptBox[\(E\), \(\[Rule]\)]\)"
]
, {t, 0, 1, 0.02}];
ListAnimate[Join[p0, p1]]
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:33, 14 October 2020 | | 480 × 536 (3.63 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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