r = size * 1.0
exponent = 1.0 / 2.0 # run with exponent=1 to get a physically correct version
doc = FieldplotDocument('naughty-solenoid')
field = Field({'coils': [[0, 0, 0, r, l, 1]]})
n = 15
for i in range(n):
a = (0.5 + i) / n
a = (-1. + 2. * a)
# ... after this, a ranges approximately from -1 to 1
a = copysign(abs(a)**exponent, a)
# unphysical version for pedagogical use, students explain why it's impossible
# makes field more intense near the walls
# re copysign, see https://stackoverflow.com/questions/1986152/why-doesnt-python-have-a-sign-function
a = a * size
line = FieldLine(field, [0.0, a], directions='both', maxr=15.0)
doc.draw_line(line, arrows_style={'dist': 3, 'offsets': [0., .5, .5, 1.]})
doc.draw_object(
'path', {
'style': 'fill:none; stroke:#808080; ' +
'stroke-width:.06; stroke-linecap:butt',
'd': f'M -{l},-{r} L {l},-{r}'
})
doc.draw_object(
'path', {
'style': 'fill:none; stroke:#808080; ' +
'stroke-width:.06; stroke-linecap:butt',
'd': f'M -{l},{r} L {l},{r}'
})
doc.write()
#!/usr/bin/python3
# This is based on the code snippet at https://commons.wikimedia.org/wiki/File:VFPt_dipole.svg .
from math import *
from vectorfieldplot import FieldplotDocument,Field,FieldLine
# ... https://github.com/CD3/VectorFieldPlot
import logging
logging.basicConfig(level=logging.ERROR) # can be DEBUG, INFO, WARNING, or ERROR
doc = FieldplotDocument('dipole', width=800, height=600, commons=True)
k=1 # 3 for first panel
field = Field({'dipoles':[[k,0,1,0]]})
n = 16
for i in range(n):
a = 2.0 * pi * (0.5 + i) / n
line = FieldLine(field, [1+k+cos(a), sin(a)],
maxr=1000, directions='both', pass_dipoles=0)
doc.draw_line(line, arrows_style=None)
doc.write()
# spacing at left side is disrupted by extra lines; if too big, disrupted by missing lines
# Presumably this is because the software uses some units for I and B; if it was SI, then I would
# expect this to be 0.5e-7...?
for i in range(m):
q = (i - m / 2.0) * 2.0 / m # ranges from -1 to 1
y = q * h
r = abs(y) + 1.0e-6
if y > 0.0:
s = 1.0
else:
s = -1.0
aa = a / f
nn = (a * r + s * log(r)) / spacing
if floor(nn) > floor(last_nn) and not (y > -1.0 / aa and y < 0.0) and not (
y < 0.0 or y > 0.225 / aa):
# ... 2nd clause is to avoid drawing the closed lines twice, 3rd is to avoid drawing lines that aren't closed
print("y=", y, ", nn=", nn)
line = FieldLine(field, [0, y], directions='both')
doc.draw_line(line,
linewidth=1,
linecolor='#ff0000',
arrows_style=None)
last_nn = nn
n = 20
for i in range(n):
q = (i - n / 2.0) * 2.0 / n # ranges from -1 to 1
y = q * h
line = FieldLine(field, [-2.9, y], directions='both')
doc.draw_line(line, linewidth=4, arrows_style=None)
doc.write()
#!/usr/bin/python3
from math import *
from vectorfieldplot import FieldplotDocument, Field, FieldLine
# ... https://github.com/CD3/VectorFieldPlot
print("generating file field-lines.svg")
# paste this code at the end of VectorFieldPlot 1.0
doc = FieldplotDocument('field-lines', width=800, height=800)
field = Field({'monopoles': [[0, -1, 1], [0, 1, -1]]})
n = 16
for i in range(n):
a = (0.5 + i) / n
a = 2.0 * pi * a
line = FieldLine(field, [0, -1],
start_v=[cos(a), sin(a)],
directions='forward')
doc.draw_line(line)
doc.write()
#!/usr/bin/python3
from math import *
from vectorfieldplot import FieldplotDocument,Field,FieldLine
# ... https://github.com/CD3/VectorFieldPlot
print("generating files u.svg, like charges")
# paste this code at the end of VectorFieldPlot 1.0
doc = FieldplotDocument('u', width=800, height=800)
field = Field({'monopoles':[[-1,0,-1], [1,0,-1]]})
doc.draw_charges(field)
for x in [-1, 1]:
line = FieldLine(field, [x,0], start_v=[x, 0],
directions='backward')
doc.draw_line(line)
n = 32
for i in range(n):
a = 2.0 * pi * (0.5 + i) / n
line = FieldLine(field, [10.*cos(a), 10.*sin(a)],
directions='forward')
doc.draw_line(line)
doc.write()
print("generating files v.svg, opposite charges")
# paste this code at the end of VectorFieldPlot 1.0
doc = FieldplotDocument('v', width=800, height=800)
field = Field({'monopoles':[[-1,0,1], [1,0,-1]]})
doc.draw_charges(field)
n = 16
for i in range(n):
'homogeneous': [field_direction],
'dipoles': [[
0, 0, 4 * pi * ball_radius**3 * field_direction[0],
4 * pi * ball_radius**3 * field_direction[1]
]]
})
n = 20
for i in range(n):
a = -3 + 6 * (0.5 + i) / n
line = FieldLine(field, [a * scale, 6 * scale], maxr=12, pass_dipoles=1)
if abs((n - 1.) / 2. - i) > 7: off = 4 * [0.5]
else: off = 4 * [0.25]
doc.draw_line(line,
arrows_style={
'min_arrows': 2,
'max_arrows': 2,
'offsets': off,
'scale': 2.0
})
# 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)
first_sphere = True
for xys in [xy0, xy1]:
for i in range(n):
if first_sphere and i >= n / 2:
continue
displ = R * (2 * (i + 0.5) / n - 1) * math.sqrt(0.5)
p0 = (displ, -displ) + xys
line = FieldLine(field,
p0,
directions='both',
maxr=7,
path_close_tol=0.2,
hmax=0.1)
doc.draw_line(line,
arrows_style={
'dist': 1.8,
'max_arrows': 2,
'offsets': [0.9, 0.3, 0.3, 0.9]
})
first_sphere = False
# draw the spherical magnets
defs = doc.draw_object('defs', {})
grad = doc.draw_object('radialGradient', {
'id': 'grad',
'r': str(1.2 * R),
'cx': '0',
'cy': str(0.2 * R),
'fx': '0',
'fy': str(0.6 * R),
'gradientUnits': 'userSpaceOnUse'
},