File:VFPt sphere-magnet potential+contour.svg
Summary
{{Information
|description=
|date=2019-09-27
|source=Own work
|author=Geek3
|permission=
|other versions=
|other fields={{Igen|VectorFieldPlot|+|c1=
- paste this code at the end of VectorFieldPlot 2.3
doc = FieldplotDocument('VFPt_sphere-magnet_potential+contour', commons=True,
width=600, height=600)
R = 1.0 c = np.array([0., 0.]) M = np.array([0., 1.]) field_outside = Field([ ['dipole', {'x':c[0], 'y':c[1], 'px':M[0]*4./3.*pi*R**3, 'py':M[1]*4./3.*pi*R**3}] ]) Bfield_inside = Field([ ['homogeneous', {'Fx':2./3.*M[0], 'Fy':2./3.*M[1]}] ]) Hfield_inside = Field([ ['homogeneous', {'Fx':-1/3.*M[0], 'Fy':-1/3.*M[1]}] ])
def spheremagnet_Bfield(xy):
if vabs(xy - c) < R:
return Bfield_inside.F(xy)
else:
return field_outside.F(xy)
def spheremagnet_potential(xy):
if vabs(xy - c) < R:
return Hfield_inside.V(xy)
else:
return field_outside.V(xy)
field = Field([ ['custom', {'F':spheremagnet_Bfield, 'V':spheremagnet_potential}] ])
U0 = field.V(c + R * vnorm(M)) doc.draw_scalar_field(func=field.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0) doc.draw_contours(func=field.V, levels=np.linspace(-U0, U0, 17)[1:-1])
nlines = 20 for iline in range(nlines):
p0 = (R * (2 * (iline + 0.5) / nlines - 1), 0.)
line = FieldLine(field, p0, directions='both', maxr=7)
if fabs(iline - (nlines - 1) / 2.) < 6.:
arst = {'at_potentials':[-1.5/8 * U0, 1.5/8 * U0]}
else:
arst = {'max_arrows':1}
doc.draw_line(line, linewidth=2.4, arrows_style=arst)
- draw the spherical magnet
g = doc.draw_object('g', {'id':'sphere',
'transform':'translate({},{})'.format(*c)})
defs = doc.draw_object('defs', {}, group=g) grad = doc.draw_object('radialGradient', {'id':'grad', 'r':str(1.2*R),
'cx':'0', 'cy':str(0.2*R), 'fx':'0', 'fy':str(0.6*R), 'gradientUnits':'userSpaceOnUse'}, group=defs)
for col, of, opa in [['#ffffff', '0', '0.8'], ['#ffffff', '0.04', '0.7'],
['#ffffff', '0.11', '0.4'], ['#ffffff', '0.22', '0.2'],
['#555555', '0.7', '0.3'], ['#000000', '1', '0.6']]:
stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
'stop-opacity':opa}, group=grad)
clip = doc.draw_object('clipPath', {'id':'circle_clip'}, group=defs) doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R)}, group=clip)
gc = doc.draw_object('g', {'clip-path':'url(#circle_clip)'}, group=g) doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
'style':'fill:#00cc00; stroke:none;'}, group=gc)
doc.draw_object('path', {'d':'M -1,0 A 1,1 0 0 0 1,0 L -1,0 Z',
'style':'fill:#ff0000; stroke:none;'}, group=gc)
text_N = doc.draw_object('text', {'text-anchor':'middle', 'x':'0', 'y':'0',
'transform':'translate({},{}) scale({},{})'.format(0, 0.56*R-0.2, 0.05, -0.05),
'style':'fill:#000000; stroke:none; ' +
'font-size:12px; font-family:Bitstream Vera Sans;'}, group=g)
text_N.text = 'N' text_S = doc.draw_object('text', {'text-anchor':'middle', 'x':'0', 'y':'0',
'transform':'translate({},{}) scale({},{})'.format(0, -0.56*R-0.2, 0.05, -0.05),
'style':'fill:#000000; stroke:none; ' +
'font-size:12px; font-family:Bitstream Vera Sans;'}, group=g)
text_S.text = 'S' doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
'style':'fill:url(#grad); stroke:none;', 'transform':'rotate(30) scale(1.4,1)'}, group=gc)
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
'style':'fill:none; stroke:#000000; stroke-width:0.04;'}, group=g)
doc.write() }} }}
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- 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.
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