# paste this code at the end of VectorFieldPlot 3.0

doc = FieldplotDocument('VFPt_horseshoe-magnet-and-wire', commons=True,
    width=600, height=600)

x0, y0 = 0.0, -1.0
h = 2.0
R = 1.0
r = 0.3

field = Field({'charged_discs':[ [x0-R-r, y0+h, x0-R+r, y0+h, -1], [x0+R-r, y0+h, x0+R+r, y0+h, 1] ], 'wires':[[0,y0+h-0.05,-0.2]]})
doc.draw_currents(field)

def startpath(t):
    return sc.array([x0 + R - R*cos(t*2*pi), y0 + h + R*sin(t*2*pi)])
def dstartpath(t):
    return (startpath(t+1e-6) - startpath(t-1e-6)) / 2e-6
def FieldSum(t0, t1):
    return 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)

n = 24
for i in range(n):
    p0 = startpos((0.5 + i) / n)
    line = FieldLine(field, p0, directions='both', maxr=1000)
    fe = [True, False, False, True]
    if i in [0, 1, 2, n-1, n-2, n-3]:
        fe = [False, False, False, False]
    min_arrows = 1
    if i == n - 7:
        min_arrows = 3
    doc.draw_line(line, arrows_style={
                  'dist':2.0, 'fixed_ends':fe, 'min_arrows':min_arrows})

doc.write()