File:VFPt superconductor ball E-field potential.svg
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Size of this PNG preview of this SVG file: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels.
Original file (SVG file, nominally 600 × 600 pixels, file size: 99 KB)
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Summary
[edit]| Description |
English: Deformation of a previously homogeneous electric field around a perfect conducting ball (e.g. iron or a superconductor). The electric field lines are accurately computed. The electric potential is drawn as a background color field. |
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| Date | |||
| Source | Own work | ||
| Author | Geek3 | ||
| Other versions |
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| SVG development |  This W3C-invalid vector image was created with Inkscape, or with something else.
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| Source code | SVG code# paste this code at the end of VectorFieldPlot 2.0
doc = FieldplotDocument('VFPt_superconductor_ball_E-field_potential',
width=600, height=600, commons=True)
unit = 100.
field_direction = [0.0, -1.0]
sphere = {'p':sc.array([0., 0.]), 'r':1.2}
field = Field([['homogeneous', {'Fx':field_direction[0], 'Fy':field_direction[1]}],
['dipole', {'x':sphere['p'][0], 'y':sphere['p'][1],
'px':4*pi*sphere['r']**3*field_direction[0],
'py':4*pi*sphere['r']**3*field_direction[1]}]])
def pot(xy):
if vabs(xy) <= sphere['r']:
return 0. # zero potential inside metal sphere
return field.V(xy)
U0 = pot([3, 3])
doc.draw_scalar_field(func=pot, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
# draw the superconducting ball
ball = doc.draw_object('g', {'id':'metal_ball'})
grad = doc.draw_object('radialGradient', {'id':'metal_spot', 'cx':'0.53', 'cy':'0.54',
'r':'0.55', 'fx':'0.65', 'fy':'0.7', 'gradientUnits':'objectBoundingBox'}, group=ball)
for col, of in (('#fff', 0), ('#e7e7e7', 0.15), ('#ddd', 0.25), ('#aaa', 0.7), ('#888', 0.9), ('#666', 1)):
doc.draw_object('stop', {'offset':of, 'stop-color':col}, group=grad)
doc.draw_object('circle', {'cx':sphere['p'][0], 'cy':sphere['p'][1], 'r':str(sphere['r']),
'style':'fill:url(#metal_spot); stroke:#000; stroke-width:0.02'}, group=ball)
ball_charges = doc.draw_object('g', {'style':'stroke-width:0.02; stroke-linecap:square'}, group=ball)
n_lines = 20
for i in range(n_lines):
a = -3 + 6 * (0.5 + i) / n_lines
line = FieldLine(field, [a, 6], maxr=12, pass_dipoles=1)
if abs((n_lines - 1.) / 2. - i) > 7:
off = {'start':0.5, 'leave_image':0.5, 'enter_image':0.5}
else:
off = {'start':0.25, 'leave_image':0.25, 'enter_image':0.25, 'end':0.25}
doc.draw_line(line, arrows_style={'min_arrows':2, 'max_arrows':2, 'offsets':off})
# draw little charge signs near the surface
path_minus = 'M {0:.5f},0 h {1:.5f}'.format(-2./unit, 4./unit)
path_plus = 'M {0:.5f},0 h {1:.5f} M 0,{0:.5f} v {1:.5f}'.format(-2./unit, 4./unit)
# check if fieldline crosses sphere surface
tlist = sc.linspace(0., 1., 101)
for i in range(1, len(tlist)):
in0 = vabs(line.get_position(tlist[i-1]) - sphere['p']) <= sphere['r']
in1 = vabs(line.get_position(tlist[i]) - sphere['p']) <= sphere['r']
if in0 != in1:
# find the point where the field line cuts the surface
t = op.brentq(lambda t: vabs(line.get_position(t)
- sphere['p']) - sphere['r'], tlist[i-1], tlist[i])
pr = line.get_position(t) - sphere['p']
cpos = 0.92 * sphere['r'] * pr / vabs(pr)
if in1:
path_d = path_minus
else:
path_d = path_plus
doc.draw_object('path', {'stroke':'black', 'd':path_d,
'transform':'translate({:.5f},{:.5f})'.format(
round(unit*cpos[0])/unit, round(unit*cpos[1])/unit)},
group=ball_charges)
doc.write()
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Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
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.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:19, 7 September 2019 | | 600 × 600 (99 KB) | Geek3 (talk | contribs) | User created page with UploadWizard |
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