File:VFPt tilted-magnets-array.svg
Summary
| 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 | |
| Source code | 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()
|
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