File:VFPt charged-rod.svg

# paste this code at the end of VectorFieldPlot 1.7
doc = FieldplotDocument('VFPt_charged-rod', width=600, height=600, commons=True)
L = 2.0
x0, y0, x1, y1 = 0., -L/2., 0., L/2.
field = Field({'charged_lines': [[x0, y0, x1, y1, 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)])
dstartpath = lambda t: (startpath(t+1e-6) - startpath(t-1e-6)) / 2e-6
FieldSum = lambda t0, t1: ig.quad(lambda t:
    sc.cross(field.F(startpath(t)), dstartpath(t)), t0, t1)[0]
Ftotal = FieldSum(0, 1)
def startpos(s):
    t = op.brentq(lambda t: FieldSum(0, t) / Ftotal - s, 0, 1)
    return startpath(t)

# plot field lines
n = 24
for i in range(n):
    p0 = startpos((0.5 + i) / n)
    line = FieldLine(field, p0, directions='both', maxr=5)
    doc.draw_line(line, arrows_style={'dist':2})

# 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 * (sc.array([x0, y0]) + sc.array([x1, y1]))
R = sc.array([x1, y1]) - M
a = atan2(R[1], R[0])
transform = 'translate({:.6g},{:.6g})'.format(M[0], M[1])
transform += ' rotate({:.6g})'.format(degrees(a))
doc.draw_object('rect', {'x':-vabs(R)-lw/2., 'width':2*vabs(R)+lw,
    'y':-D, 'height':2*D, 'transform':transform,
    'style':'fill:{:s}; stroke:none'.format(col)})
doc.draw_object('rect', {'x':-vabs(R)-lw/2., 'width':2*vabs(R)+lw,
    'y':-D, 'height':2*D, '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()