Fayl:Charge and dielectric.gif
Charge_and_dielectric.gif (480 × 536 piksel, fayl hajmi: 3,63 MB, MIME tipi: image/gif, looped, 102 frames, 10 soniya)
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Qisqa izoh
| Taʼrif |
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). |
| Sanasi | |
| Manba | https://twitter.com/j_bertolotti/status/1315975665385123842 |
| Muallif | Jacopo Bertolotti |
| Ruxsat (Bu faylning takror foydalanilishi) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.1 code
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]]
Litsenziyalash
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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| Sana/Vaqt | Miniatura | Oʻlchamlari | Foydalanuvchi | Izoh | |
|---|---|---|---|---|---|
| joriy | 14:33, 2020-yil 14-oktyabr | Miniatyurasi yoʻq | 480 × 536 (3,63 MB) | wikimediacommons>Berto | Uploaded own work with UploadWizard |
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