File:VFPt flat magnets gap potential+contour.svg

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Original file (SVG file, nominally 800 × 800 pixels, file size: 211 KB)

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Summary

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Description
English: Drawing of two homogeneously magnetized flat cylindrical magnets with exactly computed magnetic field lines. The two magnets are aligned on top of each other along the cylinder axis and with a narrow gap in-between. This configuration is often used as a dipole magnet to create a strong and roughly uniform magnetic field in the gap, for instance in cyclotrons. The magnetic scalar potential 𝜓 is shown in the background from positive (fuchsia) through zero (yellow) to negative (aqua) together with uniformely spaced equipotential lines. Note that the field lines follow the gradient of the scalar potential.
Date
Source Own work
Author Geek3
Other versions VFPt flat magnets gap potential.svg, VFPt flat magnets gap absB.svg
SVG development
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The SVG code is valid.
 
This plot was created with VectorFieldPlot.
Source code
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Python code

# paste this code at the end of VectorFieldPlot 2.4
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_flat_magnets_gap_potential+contour', commons=True,
    width=800, height=800)

Bfield = Field({'coils':[ [0, 1, pi/2, 2, 0.5 ,1],
                        [0, -1, pi/2, 2, 0.5 ,1] ]})

Hfield = Field([ ['charged_disc', {'x0':-2, 'y0':-1.5, 'x1':2, 'y1':-1.5, 'Q':-1}],
                 ['charged_disc', {'x0':-2, 'y0':-0.5, 'x1':2, 'y1':-0.5, 'Q':1}],
                 ['charged_disc', {'x0':-2, 'y0':0.5, 'x1':2, 'y1':0.5, 'Q':-1}],
                 ['charged_disc', {'x0':-2, 'y0':1.5, 'x1':2, 'y1':1.5, 'Q':1}] ])

doc.draw_magnets(Bfield)
        
U0 = Hfield.V([0., 1.5 + 0.02])
doc.draw_scalar_field(func=Hfield.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
U1 = Hfield.V([0., 1.5])
doc.draw_contours(func=Hfield.V, levels=sc.linspace(-U1, U1, 11)[1:-1])

nlines = 22
R0 = op.brentq(lambda x: Bfield.F([x, 0.])[1], 0, 3)
Sp = Startpath(Bfield, lambda t: sc.array([-R0 + 2. * R0 * t, 0.]))
xstart = [Sp.startpos((0.2+i) / (nlines-0.6))[0] for i in range(nlines)]

cond = lambda xy: fabs(xy[1]) < 1e-2 or fabs(xy[1]) > 1.4

for iline, x in enumerate(xstart):
    line = FieldLine(Bfield, [x, 0.], directions='both', maxr=12)
    doc.draw_line(line, linewidth=2.4, arrows_style={'potential':Hfield.V,
        'at_potentials':[-0.3*U1, 0., 0.3*U1], 'condition_func':cond})

for x0, y0 in ((-1, -1), (-1, 1), (1, -1), (1, 1)):
    line = FieldLine(Bfield, [2.3 * x0, 1. * y0], directions='both', maxr=5)
    doc.draw_line(line, linewidth=2.4, arrows_style={'dist':2,
        'offsets':{'start':1, 'end':0} })

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
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
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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
current09:19, 3 October 2019Thumbnail for version as of 09:19, 3 October 2019800 × 800 (211 KB)Geek3 (talk | contribs)User created page with UploadWizard

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