File:VFPt capacitor-thin-rods.svg

# paste this code at the end of VectorFieldPlot 1.6
doc = FieldplotDocument('VFPt_capacitor-thin-rods', width=800, height=600, commons=True)
l = 4.5
d = 1.5
plates = [{'x0':-l/2., 'y0':d/2., 'x1':l/2., 'y1':d/2., 'Q':1.},
          {'x0':-l/2., 'y0':-d/2., 'x1':l/2., 'y1':-d/2., 'Q':-1.}]
field = Field({'charged_lines':
    [[p['x0'], p['y0'], p['x1'], p['y1'], p['Q']] for p in plates]})

def startpath(t):
    # take an oval with stright lines and half-cirles around one plate
    tt = (t%1) * (2 * l + pi * d)
    if tt <= l*0.5:
        return sc.array([tt, d])
    elif tt <= l*0.5 + pi/2.*d:
        phi = (tt - l*0.5) / (d/2.)
        return sc.array([l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
    elif tt <= l*1.5 + pi/2.*d:
        return sc.array([l - (tt - pi/2.*d), 0.])
    elif tt <= l*1.5 + pi*d:
        phi = (tt - l*1.5) / (d/2.)
        return sc.array([-l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
    else:
        return sc.array([tt - (l*2. + pi*d), d])
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=2000.)
    doc.draw_line(line, arrows_style={'dist':2, 'min_arrows':1})

# plot rods
D = 0.055
lw = 0.01
nsign = n
plus = 'M 0,-0.02 v 0.04 M -0.02,0 h 0.04'
minus = 'M -0.02,0 h 0.04'
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)

for p in plates:
    M = 0.5 * (sc.array([p['x0'], p['y0']]) + sc.array([p['x1'], p['y1']]))
    R = sc.array([p['x1'], p['y1']]) - M
    a = atan2(R[1], R[0])
    if p['Q'] > 0:
        col = '#f00'
        sign = plus
    else:
        col = '#12f'
        sign = minus
    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':sign,
        'transform':'translate({:.6g},{:.6g})'.format(*pos),
        'style':'fill:none; stroke:#000; stroke-width:{:.6g}; '.format(2*lw) +
        'stroke-linecap:square'})

doc.write()