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 for the case of vanishing susceptibility () 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
InfoField
 The SVG code is valid.
 This plot was created with VectorFieldPlot.
Source code
InfoField

Python code

Python VectorFieldPlot 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=np.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*np.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()

Licensing

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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Under the following conditions:
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Captions

Field lines of B and grad(B) of a bar magnet

Items portrayed in this file

depicts

magnetic field

inception

28 June 2020

media type

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current20:39, 28 June 2020Thumbnail for version as of 20:39, 28 June 2020572 × 660 (92 KB)wikimediacommons>Geek3Uploaded own work with UploadWizard

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