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File:VFPt superconductor cylinder B-field potential+contour.svg

Original file ‎(SVG file, nominally 600 × 600 pixels, file size: 102 KB)

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Description
English: Deformation of a previously homogeneous magnetic field around an ideal diamagnetic infinite cylinder with very small permeability (e.g. a superconductor). Inside the cylinder the B-field vanishes, but the H-field is finite and uniform. The magnetic field lines are accurately computed. The magnetic scalar potential is drawn as a background color field and uniformely spaced equipotential lines are shown.
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Source Own work
Author Geek3
Other versions VFPt superconductor ball B-field potential+contour.svg, VFPt superconductor cylinder B-field.svg
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 2.4
doc = FieldplotDocument('VFPt_superconductor_cylinder_B-field_potential+contour',
    width=600, height=600, commons=True)

B0 = [0.0, -1.0]
sphere = {'p':sc.array([0., 0.]), 'r':1.2}

field_outside = Field([ ['homogeneous', {'Fx':B0[0], 'Fy':B0[1]}],
    ['dipole2d', {'x':sphere['p'][0], 'y':sphere['p'][1],
     'px':-2*pi*sphere['r']**2 * B0[0],
     'py':-2*pi*sphere['r']**2 * B0[1]}] ])

Hfield_inside = Field([ ['homogeneous', {'Fx':2.*B0[0], 'Fy':2.*B0[1]}] ])

def sphere_Hfield(xy):
    if vabs(xy - sphere['p']) < sphere['r']:
        return Hfield_inside.F(xy)
    else:
        return field_outside.F(xy)

def sphere_potential(xy):
    if vabs(xy - sphere['p']) < sphere['r']:
        return Hfield_inside.V(xy)
    else:
        return field_outside.V(xy)

field = Field([ ['custom', {'F':sphere_Hfield, 'V':sphere_potential}] ])

U0 = field.V([0, 3])
doc.draw_scalar_field(func=field.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
doc.draw_contours(func=field.V, levels=sc.linspace(-3.6, 3.6, 13),
    linewidth=1, linecolor='#444444')

# draw the superconducting cylinder
cylinder = doc.draw_object('g', {'id':'metal_cylinder'})

def triangle_path(phi1, phi2, r):
    x1, y1 = r * cos(radians(phi1)), r * sin(radians(phi1))
    x2, y2 = r * cos(radians(phi2)), r * sin(radians(phi2))
    d = 'M {:.4f},{:.4f}'.format(x1, y1)
    d += ' A {:.4f},{:.4f} 0 0 1 {:.4f},{:.4f}'.format(r, r, x2, y2)
    d += ' L {:.4f},{:.4f}'.format(-x2, -y2)
    d += ' A {:.4f},{:.4f} 0 0 0 {:.4f},{:.4f}'.format(r, r, -x1, -y1)
    d += ' L {:.4f},{:.4f} Z'.format(x1, y1)
    return d

def grey(bright):
    return '#' + 3 * ('%02x' % int(256. * bright - 0.5))

doc.draw_object('circle', {'cx':0, 'cy':0, 'r':'{:.4f}'.format(r),
    'style':'fill:' + grey(0.75) + '; stroke:none'}, group=cylinder)

for phi0 in [0]:
    ncolors = 25
    for a in sc.linspace(.5 / ncolors, 1 - .5 / ncolors, ncolors):
        bright = 0.75 + 0.15 * a
        phi1 = phi0 - 60 * (acos(2. * a - 1) / pi)**1.5
        phi2 = phi0 + 60 * (acos(2. * a - 1) / pi)**1.5
        d = triangle_path(phi1, phi2, r)
        doc.draw_object('path', {'d':d,
            'style':'fill:' + grey(bright) + '; stroke:none'}, group=cylinder)

doc.draw_object('circle', {'cx':0, 'cy':0, 'r':str(r),
    'style':'fill:none; stroke:black; stroke-width:0.02'}, group=cylinder)

n_lines = 20
for i in range(n_lines):
    a = -3 + 6 * (0.5 + i) / n_lines
    line = FieldLine(field, [a, 8], maxr=16, pass_dipoles=1)
    doc.draw_line(line, linewidth=2.4, arrows_style={'at_potentials':[-2.7, 2.7]})

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
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This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
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
current12:47, 13 October 2019Thumbnail for version as of 12:47, 13 October 2019600 × 600 (102 KB)Geek3 (talk | contribs)User created page with UploadWizard

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