File:VFPt bar-magnet-forces.svg
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Summary
| Description |
English: Top: Exactly computed field lines of magnetic field B of a cylindrical bar magnet with several euqipotential lines of the magnetic scalar potential. The B-field is proportional to the force exerted on external magnetic north-poles. Bottom: Exactly computed field lines of grad(abs(B)) of a cylindrical bar magnet with several euqipotential lines of abs(B). This field is proportional to the force exerted on small magnetizable particles, such as iron filings. |
| Date | |
| Source | Own work |
| Author | Geek3 |
| SVG development |  This plot was created with VectorFieldPlot. |
| Source code | Python code# paste this code at the end of VectorFieldPlot 3.2
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
docB = FieldplotDocument('VFPt_bar-magnet-forces',
commons=True, width=400, height=300)
R = 0.3
L2 = 1.
m = 1.
def bounds_func(xy):
out_magnet = min(L2 - fabs(xy[0]), R - fabs(xy[1]))
out_image = max(fabs(xy[0]) - 2.0, fabs(xy[1]) - 1.5)
return max(out_magnet, out_image)
Hfield = Field([ ['charged_disc', {'x0':-L2, 'y0':-R, 'x1':-L2, 'y1':R, 'Q':-m*.5/L2}],
['charged_disc', {'x0':L2, 'y0':-R, 'x1':L2, 'y1':R, 'Q':m*.5/L2}] ])
Bfield = Field([ ['coil', {'x':0, 'y':0, 'phi':0, 'R':R, 'Lhalf':L2, 'I':m/(R**2*pi)}] ])
phi0 = Hfield.V((L2, R/2))
rstart = 0.35
startpath = Startpath(Bfield, lambda t: array((L2-rstart*cos(t), (R+rstart)*sin(t))),
t0=asin(R/(R+rstart)), t1=2*pi-asin(R/(R+rstart)))
nlines = 16
for iline in range(nlines):
p0 = startpath.startpos((iline + 0.1) / (nlines - 0.8))
line = FieldLine(Bfield, p0, directions='both', maxr=20, bounds_func=bounds_func)
docB.draw_line(line, linewidth=2,arrows_style={'potential':Hfield.V,
'at_potentials':[Hfield.V((-1.4*L2, 2*R)), Hfield.V((1.4*L2, 2*R))]})
print('computing contours...')
#docB.draw_scalar_field(func=Hfield.V, cmap=docB.cmap_AqYlFs, vmin=-phi0, vmax=phi0)
docB.draw_contours(func=Hfield.V, linewidth=0.8, linecolor='#555555',
levels=sc.linspace(-phi0, phi0, 17))
docB.draw_object('rect', {'x':-2.005, 'y':-1.505, 'width':4.01, 'height':3.01,
'fill':'none', 'stroke':'#aaaaaa', 'stroke-width':0.03})
docB.draw_magnets(Bfield)
docB.write()
docGrad = FieldplotDocument('VFPt_bar-magnet-forces_grad',
commons=True, width=400, height=300)
def GradH(xy):
d = 1e-6
Hx0 = vabs(Hfield.F((xy[0] - d, xy[1])))
Hx1 = vabs(Hfield.F((xy[0] + d, xy[1])))
Hy0 = vabs(Hfield.F((xy[0], xy[1] - d)))
Hy1 = vabs(Hfield.F((xy[0], xy[1] + d)))
grad = array(((Hx1 - Hx0) / (2*d), (Hy1 - Hy0) / (2*d)))
return grad
Gradfield = Field([ ['custom', {'F':GradH, 'V':lambda xy: -vabs(Hfield.F(xy))}] ])
B0 = -Gradfield.V((L2, R/2))
startpath = Startpath(Gradfield, lambda t:
array((1.6*cos(2*pi*t), 0.9*sin(2*pi*t)+0.2*sin(6*pi*t))))
nlines = 32
for iline in range(nlines):
p0 = startpath.startpos((iline + 0.5) / nlines)
line = FieldLine(Gradfield, p0, directions='both', maxr=10, bounds_func=bounds_func)
docGrad.draw_line(line, linewidth=2, arrows_style={'potential':Gradfield.V,
'at_potentials':[Gradfield.V((1.4*L2, 2*R))]})
print('computing scalar field.')
#docGrad.draw_scalar_field(func=Gradfield.V, cmap=docGrad.cmap_AqYlFs, vmin=-B0, vmax=B0)
docGrad.draw_contours(func=Gradfield.V, linewidth=0.8, linecolor='#555555',
levels=B0*sc.arange(-8.5, 0)/9)
docGrad.draw_object('rect', {'x':-2.005, 'y':-1.505, 'width':4.01, 'height':3.01,
'fill':'none', 'stroke':'#aaaaaa', 'stroke-width':0.03})
docGrad.draw_magnets(Bfield)
docGrad.write()
|
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:39, 28 June 2020 | | 572 × 660 (92 KB) | Geek3 | Uploaded own work with UploadWizard |
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