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File:VFPt magnet B currents.svg

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Original file ‎(SVG file, nominally 400 × 300 pixels, file size: 35 KB)

Captions

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Summary[edit]

Description
English: Magnetic B-field inside and outside of a cylindrical bar magnet. The field is accurately computed with a magnetic current model, where atomic currents add up to an effective current around the magnet (dot symbols for current out of the image plane, cross symbols for current into image plane). Discrete field lines are drawn.
Date
Source Own work
Author Geek3
Other versions without electric current symbols
SVG development
InfoField
 
The SVG code is valid.
 
This plot was created with VectorFieldPlot.
 
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Source code
InfoField

Python code

# paste this code at the end of VectorFieldPlot 1.4
import scipy.optimize as op

M = 1.0 # magnetic moment
r = 0.65; l = 1.2
n = 10
fieldB = Field({'coils':[[0, 0, 0, r, l, M/(r**2*pi)]]})
fieldH = Field({'charged_discs':[[-l, -r, -l, r, -0.5*M/l],
                                 [ l, -r,  l, r,  0.5*M/l]]})
inside = lambda p: -min(1-fabs(p[0]/l), 1-fabs(p[1]/r))
outside = lambda p: min(1-fabs(p[0]/l), 1-fabs(p[1]/r))

for field in ['B', 'H']:
    fname = 'VFPt_magnet_' + field + {'H':'_charges', 'B':'_currents'}[field]
    doc = FieldplotDocument(fname, width=400, height=300, commons=True)
    
    for i in range(n):
        r_rel = 2 * (0.5 + i) / n - 1
        y0 = r * (r_rel + 0.16 * (r_rel - r_rel**3))
        p0 = sc.array([l, y0])
        line1 = FieldLine(fieldB, p0*(1+1e-9), directions='forward',
                          maxr=1e4, maxn=1e4, stop_funcs=2*[outside])
        doc.draw_line(line1, arrows_style={})
        
        # B-field inside magnet
        line2 = FieldLine(fieldB, p0*(1-1e-9), directions='backward',
                          stop_funcs=2*[inside])
        if field == 'B':
            doc.draw_line(line2, arrows_style={})
        
        # H-field inside magnet
        line3 = FieldLine(fieldH, p0*(1-1e-9), directions='forward',
            stop_funcs=2*[inside])
        if field == 'H':
            doc.draw_line(line3, arrows_style={
                          'min_arrows':0, 'dist':0.6, 'max_arrows':2})
        
        p1 = line3.nodes[-1]['p'] # where lines leave the magnet on the side
        if fabs(p1[1]) >= r * (1-1e-8):
            p1[1] = copysign(max(r, fabs(p1[1])), p1[1])
            line4 = FieldLine(fieldH, p1, directions='forward',
                              stop_funcs=2*[outside])
            doc.draw_line(line4, arrows_style={'max_arrows':2})
            
            p2 = line4.nodes[-1]['p'] # where lines re-enter the magnet
            line5 = FieldLine(fieldH, p2, directions='forward',
                              stop_funcs=2*[inside])
            if field == 'H':
                doc.draw_line(line5, arrows_style={
                              'min_arrows':0, 'dist':0.6, 'max_arrows':2})
            
            line6 = FieldLine(fieldB, p1*(1-1e-9), directions='backward',
                              stop_funcs=2*[inside])
            if field == 'B':
                doc.draw_line(line6, arrows_style={})
    
    doc.draw_magnets(fieldB)
    
    if field == 'H':
        m = 8
        mon = []
        for i in range(m):
            mon.append([-l, r * ((i+0.5)/m*2-1), -1])
            mon.append([l, r * ((i+0.5)/m*2-1), 1])
        fieldCharges = Field({'monopoles':mon})
        doc.draw_charges(fieldCharges, scale='{:.8f}'.format(r/m/(15./doc.unit)))
    else:
        m = 15
        rings = []
        for i in range(m):
            rings.append([l * ((i+0.5)/m*2-1), 0, 0, r, 1])
        fieldRings = Field({'ringcurrents':rings})
        doc.draw_currents(fieldRings, scale='{:.8f}'.format(l/m/(15./doc.unit)))
    
    # postprocessing: strip text and add opacity
    for el in doc.svg.iter():
        if el.tag.endswith('g'):
            if el.get('id') != None and 'magnet' in el.get('id'):
                el.set('opacity', '0.4')
        if el.tag.endswith('text'):
            el.getparent().remove(el)
        if el.tag.endswith('circle'):
            style = el.get('style')
            if style != None:
                el.set('style', style.replace('#0000ff', '#00cc00'))
    
    doc.write()

Licensing[edit]

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Date/TimeThumbnailDimensionsUserComment
current20:00, 7 May 2017Thumbnail for version as of 20:00, 7 May 2017400 × 300 (35 KB)Geek3 (talk | contribs)User created page with UploadWizard

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