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File:Equipotential by Zureks.png

Original file ‎(639 × 1,047 pixels, file size: 111 KB, MIME type: image/png)

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Description
English: Voltage distribution between two electrically charged spheres (purple = positive voltage, blue = negative voltage). The black curves show equipotential contours.
Date
Source Own work
Author Zureks
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File:Equipotential of dipole.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Equipotential by Zureks.png → File:Equipotential of dipole.svg
For more information, see Help:SVG.
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Source code edit

The image can be created with Python Matplotlib using the following code: 

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import colors

cmap = colors.ListedColormap([np.clip((2*x, 2*(1-x), 4*(x-0.5)**2), 0, 1) for x in np.linspace(0., 1., 256)])

w, h = 639, 1047
xmax = 2.36
ymax = xmax * float(h) / float(w)
vmax = 0.78
y0 = 1.0
nlevels = 21
levels = np.linspace(-vmax, vmax, nlevels)
X, Y = np.mgrid[-xmax:xmax:250j, -ymax:ymax:800j]

# potential of two point charges
V  = 1.0 / np.maximum(np.sqrt(X**2 + (Y - y0)**2), 1e-2)
V -= 1.0 / np.maximum(np.sqrt(X**2 + (Y + y0)**2), 1e-2)

# rescale potential globally to make contour areas similar
V = (np.sqrt(1 + V * V) - 1) / V

plt.figure(figsize=(w/90., h/90.)).add_axes([0, 0, 1, 1])
contf = plt.contourf(X, Y, V, levels=levels, cmap=cmap,
         vmin=-vmax*(nlevels-1.)/nlevels, vmax=vmax*(nlevels-1.)/nlevels)
cont = plt.contour(X, Y, V, levels=contf.levels, colors='k', linestyles='solid')

plt.xticks([]), plt.yticks([])
plt.gca().set_aspect(aspect='equal')
plt.gca().axis('off')
plt.text(0, -y0, u'\u2212', size=48,fontweight='bold', ha='center', va='center')
plt.text(0, y0, '+', size=48,fontweight='bold', ha='center', va='center')
plt.savefig('Equipotential_of_dipole.png')


Licensing edit

Creative Commons CC-Zero 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/TimeThumbnailDimensionsUserComment
current21:09, 16 May 2018Thumbnail for version as of 21:09, 16 May 2018639 × 1,047 (111 KB)Geek3 (talk | contribs)Replaced with analytically computed precise contour shapes. The old version which came from an FEM simulation had significant errors towards the edges, possibly because the simulation volume was chosen too small. The potential dropped much too slowly towards the image edges. In contrast, the analytic solution is very simple, as the potential is just the linear sum of two 1/r potentials.
16:37, 11 April 2010Thumbnail for version as of 16:37, 11 April 2010639 × 1,047 (32 KB)Zureks (talk | contribs){{Information |Description={{en|1=Voltage distribution between two electrically charged spheres (purple = positive voltage, blue = negative voltage). The black curves show equipotential contours.}} |Source={{own}} |Author=Zureks |Date=2010

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