File:VFPt flat magnets gap potential+contour.svg
Summary
| Description |
English: Drawing of two homogeneously magnetized flat cylindrical magnets with exactly computed magnetic field lines. The two magnets are aligned on top of each other along the cylinder axis and with a narrow gap in-between. This configuration is often used as a dipole magnet to create a strong and roughly uniform magnetic field in the gap, for instance in cyclotrons. The magnetic scalar potential 𝜓 is shown in the background from positive (fuchsia) through zero (yellow) to negative (aqua) together with uniformely spaced equipotential lines. Note that the field lines follow the gradient of the scalar potential. |
| Date | |
| Source | Own work |
| Author | Geek3 |
| Other versions | VFPt flat magnets gap potential.svg, VFPt flat magnets gap absB.svg |
| SVG development | |
| Source code | Python code# paste this code at the end of VectorFieldPlot 2.4
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_flat_magnets_gap_potential+contour', commons=True,
width=800, height=800)
Bfield = Field({'coils':[ [0, 1, pi/2, 2, 0.5 ,1],
[0, -1, pi/2, 2, 0.5 ,1] ]})
Hfield = Field([ ['charged_disc', {'x0':-2, 'y0':-1.5, 'x1':2, 'y1':-1.5, 'Q':-1}],
['charged_disc', {'x0':-2, 'y0':-0.5, 'x1':2, 'y1':-0.5, 'Q':1}],
['charged_disc', {'x0':-2, 'y0':0.5, 'x1':2, 'y1':0.5, 'Q':-1}],
['charged_disc', {'x0':-2, 'y0':1.5, 'x1':2, 'y1':1.5, 'Q':1}] ])
doc.draw_magnets(Bfield)
U0 = Hfield.V([0., 1.5 + 0.02])
doc.draw_scalar_field(func=Hfield.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
U1 = Hfield.V([0., 1.5])
doc.draw_contours(func=Hfield.V, levels=sc.linspace(-U1, U1, 11)[1:-1])
nlines = 22
R0 = op.brentq(lambda x: Bfield.F([x, 0.])[1], 0, 3)
Sp = Startpath(Bfield, lambda t: sc.array([-R0 + 2. * R0 * t, 0.]))
xstart = [Sp.startpos((0.2+i) / (nlines-0.6))[0] for i in range(nlines)]
cond = lambda xy: fabs(xy[1]) < 1e-2 or fabs(xy[1]) > 1.4
for iline, x in enumerate(xstart):
line = FieldLine(Bfield, [x, 0.], directions='both', maxr=12)
doc.draw_line(line, linewidth=2.4, arrows_style={'potential':Hfield.V,
'at_potentials':[-0.3*U1, 0., 0.3*U1], 'condition_func':cond})
for x0, y0 in ((-1, -1), (-1, 1), (1, -1), (1, 1)):
line = FieldLine(Bfield, [2.3 * x0, 1. * y0], directions='both', maxr=5)
doc.draw_line(line, linewidth=2.4, arrows_style={'dist':2,
'offsets':{'start':1, 'end':0} })
doc.write()
|
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