File:VFPt charged-rod potential+contour.svg

# paste this code at the end of VectorFieldPlot 3.1
doc = FieldplotDocument('VFPt_charged-rod_potential+contour', width=600, height=600, commons=True)
L = 2.0
x0, y0, x1, y1 = 0., -L/2., 0., L/2.
field = Field([ ['charged_line', {'x0':x0, 'y0':y0, 'x1':x1, 'y1':y1, 'Q':1.0}] ])

# start the field lines on an ellipse with the rod ends in the focal points
a = L * 0.8
b = sqrt(a**2 - (L/2.0)**2)
def startpath(t):
    phi = 2 * pi * t
    return sc.array([b * sin(phi), a * cos(phi)])
nlines = 24
startpoints = Startpath(field, startpath).npoints(nlines)

Vmax = field.V([0.05, 0.])
Vmax2 = field.V([0.045, 0.])

# plot field lines
for iline in range(nlines):
    p0 = startpoints[iline]
    line = FieldLine(field, p0, directions='both', maxr=5)
    doc.draw_line(line, arrows_style={'potential':field.V,
                  'at_potentials':[0.094*Vmax2, 0.25*Vmax2]})

doc.draw_scalar_field(field.V, cmap=doc.cmap_AqYlFs, vmin=-Vmax, vmax=Vmax)
doc.draw_contours(func=field.V, linewidth=1, linecolor='#444444',
    levels=sc.linspace(0, Vmax2, 11)[1:-1])

# plot rods
D = 0.045
lw = 0.01
nsign = 8
plus = 'M 0,-0.02 v 0.04 M -0.02,0 h 0.04'
col = '#f22'
defs = doc.draw_object('g', {})
grad = doc.draw_object('linearGradient', {'id':'grad', 'x1':'0', 'x2':'0',
    'y1':str(-D), 'y2':str(D), 'gradientUnits':'userSpaceOnUse'}, defs)
for o, c, a in ((0, '#000', 0.3), (0.3, '#999', 0.2),
                (0.8, '#fff', 0.25), (1, '#fff', 0.65)):
    doc.draw_object('stop', {'id':'grad',
         'offset':str(o), 'stop-color':c, 'stop-opacity':str(a)}, grad)

M = 0.5 * (array([x0, y0]) + array([x1, y1]))
R = array([x1, y1]) - M
r = vabs(R)
phi = atan2(R[1], R[0])
transform = 'translate({:.6g},{:.6g})'.format(M[0], M[1])
transform += ' rotate({:.6g})'.format(degrees(phi))
path = 'M {},{}'.format(-r, -D)
path += ' H {}'.format(r)
path += ' A {},{} 0 0 1 {},{}'.format(D, D, r, D)
path += ' H {}'.format(-r)
path += ' A {},{} 0 0 1 {},{}'.format(D, D, -r, -D)
path += ' Z'
doc.draw_object('path', {'d':path, 'transform':transform,
    'style':'fill:{:s}; stroke:none'.format(col)})
doc.draw_object('path', {'d':path, 'transform':transform,
    'style':'fill:url(#grad); stroke:#000; stroke-width:{:.6g}'.format(lw)})
for i in range(nsign):
    pos = M + R * (2 * (i + 0.5) / nsign - 1)
    doc.draw_object('path', {'d':plus,
    'transform':'translate({:.6g},{:.6g})'.format(*pos),
    'style':'fill:none; stroke:#000; stroke-width:{:.6g}; '.format(2*lw) +
    'stroke-linecap:square'})

doc.write()