# paste this code at the end of VectorFieldPlot 3.1
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
doc = FieldplotDocument('VFPt_ringmagnet2',
    commons=True, width=600, height=600)

r0 = 1.0
r1 = 2.0
h = 0.5
field = Field([ ['coil', {'x':0, 'y':0, 'phi':pi/2, 'R':r1, 'Lhalf':h, 'I':1}],
         ['coil', {'x':0, 'y':0, 'phi':pi/2, 'R':r0, 'Lhalf':h, 'I':-1}] ])
n_out = 24
for i in range(n_out):
    s = (i + 0.5) / n_out * 2. - 1.
    line = FieldLine(field, [copysign(r1 + h * (1. / s**2 - 1.), s), 0.],
        directions='both', maxr=1e3)
    doc.draw_line(line, linewidth=2.4, arrows_style={'scale':1.1,
        'potential':lambda xy: xy[1] * (1-fabs(xy[0]/2.5)**2.5-fabs(xy[1]/2)**2.5),
        'at_potentials':[0], 'condition_func':lambda xy: fabs(xy[1]) > 0.7 or
            (fabs(xy[0]) > r1 and fabs(xy[1]) < 1e-4)})

n_in = 12
for i in range(n_in):
    a = (i + 0.5) / n_in * 2. - 1.
    line = FieldLine(field, [r0 * (1.2*a - 0.2*a**3), 0.],
        directions='both')
    doc.draw_line(line, linewidth=2.4, arrows_style={'scale':1.1,
        'potential':lambda xy: xy[1], 'at_potentials':[0],
        'condition_func':lambda xy: fabs(xy[0]) < r0})

# draw the magnet manually
colors = ['#00cc00', '#ff0000']
defs = doc.draw_object('defs', {})
grad = doc.draw_object('linearGradient', {'id':'grad',
    'x1':str(r0), 'x2':str(-r0), 'y1':'0', 'y2':'0',
    'gradientUnits':'userSpaceOnUse'}, group=defs)
for col, of, opa in [['#000000', '0', '0.125'],
    ['#ffffff', '0.07', '0.125'], ['#ffffff', '0.25', '0.5'],
    ['#ffffff', '0.6', '0.2'], ['#000000', '1', '0.33']]:
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad)
mag = doc.draw_object('g', {'id':'magnet'}, bg=True)
for i in [0, 1]:
    rect = doc.draw_object('rect', group=mag)
    for attr, val in [['x', -r0], ['y', [-h, 0][i]],
        ['width', 2*r0], ['height', [2*h, h][i]],
        ['style', 'fill:{0}; stroke:none'.format(colors[i])]]:
        rect.set(attr, str(val))
rect = doc.draw_object('rect', group=mag)
for attr, val in [['x', -r0], ['y', -h],
    ['width', 2 * r0], ['height', 2 * h],
    ['style', 'fill:url(#grad); stroke-width:0.04; stroke-linejoin:miter; stroke:#000000']]:
    rect.set(attr, str(val))

for x0 in [-r1, r0]:
    mag = doc.draw_object('g')
    for i in [0, 1]:
        rect = doc.draw_object('rect', group=mag)
        for attr, val in [['x', x0], ['y', [-h, 0][i]],
            ['width', r1 - r0], ['height', [2*h, h][i]],
            ['style', 'fill:{0}; stroke:none'.format(
            ['#49da49', '#ff4949'][i])]]:
            rect.set(attr, str(val))
    rect = doc.draw_object('rect', group=mag)
    for attr, val in [['x', x0], ['y', -h],
        ['width', r1 - r0], ['height', 2 * h],
        ['style', 'fill:none; stroke-width:0.04; stroke-linejoin:miter; stroke:#000000']]:
        rect.set(attr, str(val))

doc.write()