File:VFPt flat magnets gap.svg

Summary

Description
English: Drawing of two homogeneously magnetized flat cylindrical magnets with exactly computed magnetic field lines for the case of vanishing susceptibility (). 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.
Date
Source Own work
Author Geek3
Other versions field strength potential potential
SVG development
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This plot was created with VectorFieldPlot.
Category:Valid SVG created with VectorFieldPlot code#VFPt%20flat%20magnets%20gap.svg
 
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Source code
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Python code

Python VectorFieldPlot code
# paste this code at the end of VectorFieldPlot 1.10
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_flat_magnets_gap', commons=True,
    width=800, height=800)
field = Field({'coils':[[0, 1, pi/2, 2, 0.5 ,1],
                        [0, -1, pi/2, 2, 0.5 ,1]]})

doc.draw_magnets(field)

# distribute field lines proportionally to the field strength at y=0
x0 = op.brentq(lambda x: field.F([x, 0.])[1], 0, 3)
Fsum = ig.quad(lambda x: field.F([x, 0.])[1], -x0, x0)[0]
nlines = 22
xstart = [op.brentq(lambda xs: ig.quad(lambda x: field.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(field, [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(field, [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})

doc.write()

Licensing

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Category:CC-BY-SA-4.0#VFPt%20flat%20magnets%20gap.svg
Category:Self-published work Category:Field lines around magnets (image set) Category:Field lines around magnets Category:Photos by User:Geek3 Category:Bending magnets Category:Dipole magnet
Category:Bending magnets Category:CC-BY-SA-4.0 Category:Dipole magnet Category:Field lines around magnets Category:Field lines around magnets (image set) Category:Photos by User:Geek3 Category:Self-published work Category:Valid SVG created with VectorFieldPlot code