File:VFPt horseshoe-magnet.svg

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Summary

Description

English: Drawing of a horseshoe magnet with precisely computed magnetic field lines. The horseshoe magnet is assumed as a curved cylindrical rod with constant magnetisation along the cylinder axis. North- and southpole of the magnet are marked in red and green, respectively. The shape of the magnetic field is computed as follows: H- and B-field are identical in free space, so we can choose the easier one, which is the H-field. The H-field has its sources and sinks where the lines of the magnetisation end and begin. Thus, the correct field is obtained by placing magnetic charges at the surfaces of the two magnetic poles. The field of a charge disc distribution is obtained by numerical integration. The shape of the field lines is traced with a Runge-Kutta algorithm. The density of field lines corresponds roughly to the field strength, however due to 3D variations of the field, this cannot exactly be fulfilled.
Note that in measured field distributions, e.g. using magnetised iron filings the field shape in the lower part of the image (where the magnet is bent) may somewhat differ. This is because the total field strength is very weak there. Therefore any inhomogeneity in the magnetisation can strongly alter the field direction.

Date

7 July 2018

Source

Own work

Author

Geek3

SVG development

The SVG code is valid.

This plot was created with VectorFieldPlot.

This file uses embedded text.

Quality image

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Source code

Python code

# paste this code at the end of VectorFieldPlot 3.0
doc = FieldplotDocument('VFPt_horseshoe-magnet', commons=True,
    width=600, height=600)

x0, y0 = 0.0, -1.0
h = 2.0
R = 1.0
r = 0.3

# Note: The H-field of a magnet with constant profile and magnetization
# is exactly equal to the one created by magnetic surface charges
# at the ends of the magnet. In this case the ends are round discs.
field = Field([
    ['charged_disc', {'x0':x0-R-r, 'y0':y0+h, 'x1':x0-R+r, 'y1':y0+h, 'Q':-1}],
    ['charged_disc', {'x0':x0+R-r, 'y0':y0+h, 'x1':x0+R+r, 'y1':y0+h, 'Q':1}] ])

nlines = 24
def startp(t):
    return sc.array([x0 + R - R*cos(t*2*pi), y0 + h + R*sin(t*2*pi)])
startpoints = Startpath(field, startp).npoints(nlines)

for iline, p0 in enumerate(startpoints):
    line = FieldLine(field, p0, directions='both', maxr=1000)
    fe = {'start':True, 'leave_image':False, 'enter_image':False, 'end':True}
    if iline in [0, 1, 2, nlines-1, nlines-2, nlines-3]:
        fe['start'] = fe['end'] = False
    min_arrows = 1
    if iline == nlines - 7:
        min_arrows = 3
    doc.draw_line(line, arrows_style={
                  'dist':2.0, 'fixed_ends':fe, 'min_arrows':min_arrows})

# draw a horseshoe magnet with color gradients
g = doc.draw_object('g', {'id':'horseshoe',
    'transform':'translate({},{})'.format(x0, y0)})
defs = doc.draw_object('defs', {}, group=g)
grad_col = ['#000000', '#ffffff', '#ffffff', '#ffffff', '#000000']
grad_offs = sc.array([0, 0.07, 0.25, 0.6, 1])
grad_opa = sc.array([0.125, 0.125, 0.5, 0.2, 0.33])
grad1 = doc.draw_object('linearGradient', {'id':'grad1', 'x1':'0',
    'x2':'1', 'y1':'0', 'y2':'0', 'gradientUnits':'objectBoundingBox'},
    group=defs)
for col, of, opa in zip(grad_col, grad_offs, grad_opa):
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad1)
grad2 = doc.draw_object('radialGradient', {'id':'grad2', 'r':str(R+r),
    'cx':'0', 'cy':'0', 'fx':'0', 'fy':'0',
    'gradientUnits':'userSpaceOnUse'}, group=defs)
for col, of, opa in sorted(zip(grad_col, 1-grad_offs*2.*r/(R+r), grad_opa),
                           key=lambda x: x[1]):
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad2)
grad3 = doc.draw_object('radialGradient', {'id':'grad3', 'r':str(R+r),
    'cx':'0', 'cy':'0', 'fx':'0', 'fy':'0',
    'gradientUnits':'userSpaceOnUse'}, group=defs)
for col, of, opa in zip(grad_col, (R-r)/(R+r)+grad_offs*2.*r/(R+r), grad_opa):
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad3)
grad4 = doc.draw_object('linearGradient', {'id':'grad4', 'x1':str(-R-r),
    'x2':str(R+r), 'y1':'0', 'y2':'0', 'gradientUnits':'userSpaceOnUse'},
    group=defs)
for col, of, opa in [['#ffffff', '0', '1'], ['#ffffff', str(r/(R+r)), '1'],
        ['#ffffff', str(R/(R+r)), '0'], ['#ffffff', '1', '0']]:
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad4)
mask4 = doc.draw_object('mask', {'id':'mask4', 'maskContentUnits':'userSpaceOnUse'}, group=defs)
doc.draw_object('rect', {'x':str(-R-r), 'y':str(-R-r), 'width':str(2*(R+r)),
    'height':str(R+r), 'style':'fill:url(#grad4); stroke:none;'}, group=mask4)
grad5 = doc.draw_object('linearGradient', {'id':'grad5', 'x1':str(-R-r),
    'x2':str(R+r), 'y1':'0', 'y2':'0', 'gradientUnits':'userSpaceOnUse'},
    group=defs)
for col, of, opa in [['#ffffff', '0', '0'], ['#ffffff', str(r/(R+r)), '0'],
        ['#ffffff', str(R/(R+r)), '1'], ['#ffffff', '1', '1']]:
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad5)
mask5 = doc.draw_object('mask', {'id':'mask5', 'maskContentUnits':'userSpaceOnUse'}, group=defs)
doc.draw_object('rect', {'x':str(-R-r), 'y':str(-R-r), 'width':str(2*(R+r)),
    'height':str(R+r), 'style':'fill:url(#grad5); stroke:none;'}, group=mask5)

d = ('M {},{} L {},{} L {},{} A {},{} {} {} {} {},{} L {},{} L {},{} ' +
     'L {},{} A {},{} {} {} {} {},{} L {},{} Z').format(-R-r, h,
     -R+r, h, -R+r, 0, R-r, R-r, 0, 0, 1, R-r, 0, R-r, h, R+r, h, R+r, 0,
     R+r, R+r, 0, 0, 0, -R-r, 0, -R-r, h)
doc.draw_object('path', {'d':d, 'style':'fill:#ff0000; ' +
     'stroke:none;'}, group=g)
d = ('M {},{} L {},{} L {},{} A {},{} {} {} {} {},{} ' +
     'L {},{} A {},{} {} {} {} {},{} L {},{} Z').format(-R-r, h,
     -R+r, h, -R+r, 0, R-r, R-r, 0, 0, 1, 0, -R+r, 0, -R-r,
    R+r, R+r, 0, 0, 0, -R-r, 0, -R-r, h)
doc.draw_object('path', {'d':d, 'style':'fill:#00cc00;stroke:none;'},
    group=g)
d = ('M {},{} L {},{} L {},{} L {},{} L {},{} Z').format(-R-r, h,
     -R+r, h, -R+r, 0, -R-r, 0, -R-r, h)
doc.draw_object('path', {'d':d, 'style':'fill:url(#grad1);stroke:none;'},
    group=g)
d = ('M {},{} L {},{} L {},{} L {},{} L {},{} Z').format(R-r, h,
     R+r, h, R+r, 0, R-r, 0, R-r, h)
doc.draw_object('path', {'d':d, 'style':'fill:url(#grad1);stroke:none;'},
    group=g)
d = ('M {},{} L {},{} A {},{} {} {} {} {},{} ' +
     'L {},{} A {},{} {} {} {} {},{} Z').format(-R-r, 0, -R+r, 0,
    R-r, R-r, 0, 0, 1, R-r, 0, R+r, 0, R+r, R+r, 0, 0, 0, -R-r, 0)
doc.draw_object('path', {'d':d, 'style':'fill:url(#grad2);stroke:none;',
    'mask':'url(#mask4)'}, group=g)
d = ('M {},{} L {},{} A {},{} {} {} {} {},{} ' +
    'L {},{} A {},{} {} {} {} {},{} Z').format(-R-r, 0, -R+r, 0,
    R-r, R-r, 0, 0, 1, R-r, 0, R+r, 0, R+r, R+r, 0, 0, 0, -R-r, 0)
doc.draw_object('path', {'d':d, 'style':'fill:url(#grad3);stroke:none;',
    'mask':'url(#mask5)'}, group=g)
d = ('M {},{} L {},{} L {},{} A {},{} {} {} {} {},{} L {},{} L {},{} ' +
    'L {},{} A {},{} {} {} {} {},{} L {},{} Z').format(-R-r, h,
    -R+r, h, -R+r, 0, R-r, R-r, 0, 0, 1, R-r, 0, R-r, h, R+r, h, R+r, 0,
    R+r, R+r, 0, 0, 0, -R-r, 0, -R-r, h)
doc.draw_object('path', {'d':d, 'style':'fill:none; ' +
     'stroke:#000000; stroke-width:0.04;'}, group=g)

text_N = doc.draw_object('text', {'text-anchor':'middle', 'x':'0', 'y':'0',
    'transform':'translate({},{}) scale({},{})'.format(R, h-0.6, 0.04, -0.04),
    '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(-R, h-0.6, 0.04, -0.04),
    'style':'fill:#000000; stroke:none; ' +
    'font-size:12px; font-family:Bitstream Vera Sans;'}, group=g)
text_S.text = 'S'

doc.write()

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

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.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

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

	Date/Time	Thumbnail	Dimensions	User	Comment
current	18:03, 7 July 2018		600 × 600 (40 KB)	Geek3	User created page with UploadWizard

File usage

The following page uses this file:

Horseshoe magnet

Global file usage

The following other wikis use this file:

Usage on bn.wikibooks.org
- উইকিশৈশব:ইংরেজি বর্ণমালায় বিজ্ঞান/M
Usage on de.wikipedia.org
- Hufeisenmagnet
Usage on en.wikibooks.org
- Wikijunior:Science Alphabet/M
Usage on hi.wikipedia.org
- सदस्य:S7895/प्रयोगपृष्ठ
Usage on pl.wikipedia.org
- Magnes
Usage on ru.wikipedia.org
- Постоянный магнит
Usage on shn.wikibooks.org
- Wikijunior:တူဝ်မႄႈလိၵ်ႈ ပၢႆးသၢႆႊ/M

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Short title	VFPt_horseshoe-magnet
Image title	VFPt_horseshoe-magnet created with VectorFieldPlot 1.7 https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot about: https://commons.wikimedia.org/wiki/File:VFPt_horseshoe-magnet.svg rights: Creative Commons Attribution ShareAlike 4.0
Width	600
Height	600

File:VFPt horseshoe-magnet.svg

Summary

Python code

Licensing

Captions

Items portrayed in this file

depicts

horseshoe magnet

creator

some value

copyright status

copyrighted

copyright license

Creative Commons Attribution-ShareAlike 4.0 International

Commons quality assessment

Wikimedia Commons quality image

source of file

original creation by uploader

inception

7 July 2018

media type

image/svg+xml

File history

File usage

Global file usage

Metadata