# paste this code at the end of VectorFieldPlot 2.3
doc = FieldplotDocument('VFPt_superconductor_ball_B-field_potential+contour',
    width=600, height=600, commons=True)

B0 = [0.0, -1.0]
sphere = {'p':sc.array([0., 0.]), 'r':1.2}

field_outside = Field([ ['homogeneous', {'Fx':B0[0], 'Fy':B0[1]}],
    ['dipole', {'x':sphere['p'][0], 'y':sphere['p'][1],
     'px':-2*pi*sphere['r']**3 * B0[0],
     'py':-2*pi*sphere['r']**3 * B0[1]}] ])

Hfield_inside = Field([ ['homogeneous', {'Fx':1.5*B0[0], 'Fy':1.5*B0[1]}] ])

def sphere_Hfield(xy):
    if vabs(xy - sphere['p']) < sphere['r']:
        return Hfield_inside.F(xy)
    else:
        return field_outside.F(xy)

def sphere_potential(xy):
    if vabs(xy - sphere['p']) < sphere['r']:
        return Hfield_inside.V(xy)
    else:
        return field_outside.V(xy)

field = Field([ ['custom', {'F':sphere_Hfield, 'V':sphere_potential}] ])

U0 = field.V([0, 3])
doc.draw_scalar_field(func=field.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)
doc.draw_contours(func=field.V, levels=sc.linspace(-3.6, 3.6, 13))

# draw the superconducting ball
ball = doc.draw_object('g', {'id':'metal_ball'})
grad = doc.draw_object('radialGradient', {'id':'metal_spot', 'cx':'0.53', 'cy':'0.54',
    'r':'0.55', 'fx':'0.65', 'fy':'0.7', 'gradientUnits':'objectBoundingBox'}, group=ball)
for col, of in (('#fff', 0), ('#e7e7e7', 0.15), ('#ddd', 0.25), ('#aaa', 0.7), ('#888', 0.9), ('#666', 1)):
    doc.draw_object('stop', {'offset':of, 'stop-color':col}, group=grad)

doc.draw_object('circle', {'cx':sphere['p'][0], 'cy':sphere['p'][1], 'r':str(sphere['r']),
    'style':'fill:url(#metal_spot); stroke:#000; stroke-width:0.02'}, group=ball)

n_lines = 20
for i in range(n_lines):
    a = -3 + 6 * (0.5 + i) / n_lines
    line = FieldLine(field, [a, 6], maxr=12, pass_dipoles=1)
    doc.draw_line(line, linewidth=2.4, arrows_style=
        {'at_potentials':[-2.1, 2.1]})

doc.write()