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File:VFPt flat magnets gap potential.svg

Original file ‎(SVG file, nominally 800 × 800 pixels, file size: 183 KB)

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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). Note that the field lines follow the gradient of the scalar potential.
Date
Source Own work
Author Geek3
Other versions field lines field strength potential
SVG development
InfoField
 
The source code of this SVG is invalid due to VectorFieldPlot errors.
 
This W3C-invalid vector image was created with Inkscape, or with something else.

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Source code
InfoField

SVG code

# paste this code at the end of VectorFieldPlot 2.2
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_flat_magnets_gap_potential', 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)

# distribute field lines proportionally to the field strength at y=0
x0 = op.brentq(lambda x: Bfield.F([x, 0.])[1], 0, 3)
Fsum = ig.quad(lambda x: Bfield.F([x, 0.])[1], -x0, x0)[0]
nlines = 22
xstart = [op.brentq(lambda xs: ig.quad(lambda x: Bfield.F([x, 0.])[1],
    -x0, xs)[0] / Fsum - (0.2+i)/(nlines-0.6), -x0, x0) for i in range(nlines)]

for i, x in enumerate(xstart):
    line = FieldLine(Bfield, [x, 0.], directions='both', maxr=12)
    if i < 2 or nlines - i <= 2:
        min_arrows = 4
    else:
        min_arrows = 3
    doc.draw_line(line, arrows_style={'dist':3, 'min_arrows':min_arrows,
        'offsets':[1, 0.5, 0.5, 0], 'scale':1.3})

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, arrows_style={'dist':2,
        'offsets':[1, 0.5, 0.5, 0], 'scale':1.3})
        
U0 = Hfield.V([0., 1.5 + 0.02])
doc.draw_scalar_field(func=Hfield.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)

doc.write()

Licensing edit

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
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Date/TimeThumbnailDimensionsUserComment
current14:24, 21 September 2019Thumbnail for version as of 14:24, 21 September 2019800 × 800 (183 KB)Geek3 (talk | contribs)User created page with UploadWizard

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