File:VFPt tilted-magnets-array potential+contour.svg

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Original file ‎(SVG file, nominally 800 × 600 pixels, file size: 197 KB)

Captions

Captions

Field and potential of array of tilted magnets

Summary

[edit]
Description
English: Accurately computed magnetic field and scalar potential of an infinite array of tilted bar magnets. Such configuration is often used in magnet motor perpetual motion machine designs with the intention to produce a continuous field along the transversal direction. Contrary to naive imagination, the field doesn't emerge along the magnet axes, but perpendicular to the whole array. The potential is periodic in transversal direction, so that no work can be done by moving magnetic poles along the array.
Date
Source Own work
Author Geek3
Other versions VFPt tilted-magnets-array.svg
SVG development
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The SVG code is valid.
 
This plot was created with VectorFieldPlot.
Source code
InfoField

Python code

# paste this code at the end of VectorFieldPlot 3.1
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_tilted-magnets-array_potential+contour',
    commons=True, width=800, height=600)

x0, y0 = 0, -1.7
phi = pi/4
dx = 2
R = 0.4
L2 = 1.3
m = 1
Nmag = 101
xarr = x0 + sc.arange(-(Nmag//2)*dx, ((Nmag+1)//2)*dx, dx)

discs = []
Q = m / (2 * L2)
for x in xarr:
    if fabs(x) <= 10:
        p0 = array([x, y0]) + rot([-L2,R], phi)
        p1 = array([x, y0]) + rot([-L2,-R], phi)
        discs.append(['charged_disc', {'x0':p0[0], 'y0':p0[1], 'x1':p1[0], 'y1':p1[1], 'Q':-Q}])
        p0 = array([x, y0]) + rot([L2,R], phi)
        p1 = array([x, y0]) + rot([L2,-R], phi)
        discs.append(['charged_disc', {'x0':p0[0], 'y0':p0[1], 'x1':p1[0], 'y1':p1[1], 'Q':Q}])
    else:
        # save computing time using simpler pole model for remote magnets
        p0 = array([x, y0]) + rot([-L2, 0], phi)
        discs.append(['monopole', {'x':p0[0], 'y':p0[1], 'Q':-Q}])
        p1 = array([x, y0]) + rot([L2, 0], phi)
        discs.append(['monopole', {'x':p1[0], 'y':p1[1], 'Q':Q}])

fieldH = Field(discs)
fieldB = Field([ ['coil', {'x':x, 'y':y0, 'phi':phi, 'R':R, 'Lhalf':L2,
    'I':m/(R**2*pi)}] for x in xarr])
field_symbols = Field([ ['coil', {'x':x, 'y':y0, 'phi':phi, 'R':R, 'Lhalf':L2,
    'I':m/(R**2*pi)}] for x in xarr if fabs(x) < 4 + L2])

doc.draw_magnets(field_symbols)
U0 = fieldH.V(array([x0, y0]) + rot([L2, 0], phi))

def bounds(xy):
    dmax = -1
    for i in range(Nmag):
        r = xy - array([xarr[i], y0])
        r = rot(r, -phi)
        dmax = max(dmax, min(1-fabs(r[0]/L2), 1-fabs(r[1]/R)))
    return dmax

nlines = 6
xoff = 0.1
for iline in range(Nmag * nlines):
    for y, di, s in (4, 'backward', 1), (2*y0-4, 'forward', -1):
        xstart = x0 + s * xoff + dx * (iline / nlines - Nmag // 2)
        if fabs(xstart) < 4.5:
            p0 = [xstart, y]
            line = FieldLine(fieldH, p0, directions=di, maxr=8.,
                bounds_func=bounds)
            doc.draw_line(line, linewidth=2.4, arrows_style=
                {'at_potentials':[-0.4 * U0, 0.23 * U0], 'potential':fieldH.V})

nlines2 = 12
for imag in range(Nmag):
    xmag = dx * (imag - Nmag // 2)
    for iline in range(nlines2):
        a = (iline + 0.5) / nlines2
        a += -0.4 * (((2 * a - 1)**3 + 1) / 2 - a)
        p1 = rot([-0.36*L2, -R], phi)
        p2 = array([dx, 0]) + rot([0.36*L2, R], phi)
        xstart = xmag + p1[0] + a * (p2[0] - p1[0])
        ystart = y0 + p1[1] + a * (p2[1] - p1[1])
        if fabs(xstart) < 4.5:
            line = FieldLine(fieldH, [xstart, ystart], directions='both', maxr=2*L2,
                stop_funcs=2*[bounds])
            doc.draw_line(line, linewidth=2.4, arrows_style=
                {'max_arrows':1, 'min_arrows':1})

print('computing scalar field.')
doc.draw_scalar_field(func=fieldH.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
doc.draw_contours(func=fieldH.V, linewidth=1, linecolor='#111111',
    levels=sc.linspace(-U0, U0, 17)[1:-1], attributes={'opacity':'0.7'})

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
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
  • 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/TimeThumbnailDimensionsUserComment
current21:23, 13 June 2020Thumbnail for version as of 21:23, 13 June 2020800 × 600 (197 KB)Geek3 (talk | contribs)Uploaded own work with UploadWizard

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