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File:VFPt tilted-magnets-array.svg

Original file ‎(SVG file, nominally 800 × 600 pixels, file size: 66 KB)

Captions

Captions

Field of array of tilted magnets

Summary

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Description
English: Accurately computed magnetic field of an infinite array of tilted bar magnets. Such configuration is often used in magnet motor 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. Transversally to the array, the field is mostly orthogonal.
Date
Source Own work
Author Geek3
Other versions VFPt tilted-magnets-array potential+contour.svg
SVG development
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This plot was created with VectorFieldPlot.
Source code
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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',
    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, 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, arrows_style=
                {'max_arrows':1, 'min_arrows':1})

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
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
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Date/TimeThumbnailDimensionsUserComment
current21:23, 13 June 2020Thumbnail for version as of 21:23, 13 June 2020800 × 600 (66 KB)Geek3 (talk | contribs)Uploaded own work with UploadWizard

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