File:VFPt capacitor-infinite-plate potential.svg

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Original file (SVG file, nominally 800 × 600 pixels, file size: 135 KB)

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Summary

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Description
English: Electric field of simple parallel plate capacitor. The capacitor consists of two parallel rectangular plates perpendicular the the image plane and expanding to infinity. The field is accurately computed for a uniform charge distribution on each plate, but therefore the potential on each plate is not exactly constant. The potential at each position is plotted as the background color from positive (fuchsia) through neutral (yellow) to negative (aqua).
Date
Source Own work
Author Geek3
SVG development
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This plot was created with VectorFieldPlot.
Source code
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Python code

# paste this code at the end of VectorFieldPlot 2.1
doc = FieldplotDocument('VFPt_capacitor-infinite-plate_potential',
    width=800, height=600, commons=True)
l = 4.5
d = 1.5
plates = [{'x0':-l/2., 'y0':d/2., 'x1':l/2., 'y1':d/2., 'q':1.},
          {'x0':-l/2., 'y0':-d/2., 'x1':l/2., 'y1':-d/2., 'q':-1.}]
field = Field([ ['charged_plane', plates[0] ], ['charged_plane', plates[1] ] ])

def startpath(t):
    # take an oval with stright lines and half-cirles around one plate
    tt = (t%1) * (2 * l + pi * d)
    if tt <= l*0.5:
        return sc.array([tt, d])
    elif tt <= l*0.5 + pi/2.*d:
        phi = (tt - l*0.5) / (d/2.)
        return sc.array([l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
    elif tt <= l*1.5 + pi/2.*d:
        return sc.array([l - (tt - pi/2.*d), 0.])
    elif tt <= l*1.5 + pi*d:
        phi = (tt - l*1.5) / (d/2.)
        return sc.array([-l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
    else:
        return sc.array([tt - (l*2. + pi*d), d])

nlines = 22
startpoints = Startpath(field, startpath).npoints(nlines)

# plot field lines
for p0 in startpoints:
    line = FieldLine(field, p0, directions='both')
    doc.draw_line(line, arrows_style={'dist':2, 'min_arrows':1})

# plot capacitor plate
D = 0.055
lw = 0.01
nsign = nlines
plus = 'M 0,-0.02 v 0.04 M -0.02,0 h 0.04'
minus = 'M -0.02,0 h 0.04'
for p in plates:
    M = 0.5 * (sc.array([p['x0'], p['y0'] ]) + sc.array([p['x1'], p['y1'] ]))
    R = sc.array([p['x1'], p['y1'] ]) - M
    a = atan2(R[1], R[0])
    if p['q'] > 0:
        col = '#e22'
        sign = plus
    else:
        col = '#45e'
        sign = minus
    transform = 'translate({:.6g},{:.6g})'.format(M[0], M[1])
    transform += ' rotate({:.6g})'.format(degrees(a))
    doc.draw_object('rect', {'x':-vabs(R)-lw/2., 'width':2*vabs(R)+lw,
        'y':-D, 'height':2*D,
        'style':'fill:{:s}; stroke:#000; stroke-width:{:.6g}'.format(col, lw),
        'transform':transform})
    for i in range(nsign):
        pos = M + R * (2 * (i + 0.5) / nsign - 1)
        doc.draw_object('path', {'d':sign,
        'transform':'translate({:.6g},{:.6g})'.format(*pos),
        'style':'fill:none; stroke:#000; stroke-width:{:.6g}; '.format(2*lw) +
        'stroke-linecap:square'})

# draw potential
U0 = field.V([0., d/2. + D + lw/2.])
doc.draw_scalar_field(func=field.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)

doc.write()


Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current14:32, 14 September 2019Thumbnail for version as of 14:32, 14 September 2019800 × 600 (135 KB)Geek3 (talk | contribs)User created page with UploadWizard

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