from math import *
from vectorfieldplot import FieldplotDocument, Field, FieldLine
# ... https://github.com/CD3/VectorFieldPlot
# based on https://commons.wikimedia.org/wiki/File:VFPt_cylindrical_coil.svg
# author Geek3, GFDL
size = 0.6
proportion = 4
l = size * proportion
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', {
#!/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()
#!/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 a.svg")
# paste this code at the end of VectorFieldPlot 1.0
doc = FieldplotDocument('a', width=600, height=600, commons=True)
#field = Field({'homogeneous':[[1,3]]})
a = 0.33 # ratio of constant field to current in wire
curr = 0.045 # current in wire
field = Field({'wires': [[0, 0, -curr]], 'homogeneous': [[a * curr, 0]]})
m = 10000 # controls resolution of search for appropriate starting points
# spacing of field lines is dr/di propto 1/B propto r; this integrates to r=(const)exp(const*i)
h = 3 # half-height of square box; is this right?
spacing = 0.01 # extra factor to scale spacing, smaller gives smaller spacing
last_nn = 999
f = 0.2 # .235 was too big
# why is this needed???; bigger f excludes more double-counted lines; if f is too small, uniform
# 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
#!/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):
#!/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):
a = (0.5 + i) / n
a = 2.0 * pi * a
#!/usr/bin/python3
# https://commons.wikimedia.org/wiki/File:VFPt_superconductor_ball_E-field.svg
# Original code by Geek3, CC-BY. Modifications by B. Crowell under the same license.
from math import *
from vectorfieldplot import FieldplotDocument, Field, FieldLine
# ... https://github.com/CD3/VectorFieldPlot
scale = 1
doc = FieldplotDocument('hw-conducting-sphere-in-uniform-field',
width=600,
height=600)
field_direction = [0.0, -1.0]
ball_radius = 1.2 * scale
field = Field({
'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={
#!/usr/bin/python3
from math import *
from vectorfieldplot import FieldplotDocument, Field, FieldLine
# ... https://github.com/CD3/VectorFieldPlot
print("generating files a.svg")
# paste this code at the end of VectorFieldPlot 1.0
s = 1 # scale-down factor
doc = FieldplotDocument('a', unit=100 / s)
m = [[-0.3, 0, 1], [0.5, 0, -1], [0, -0.3, -1], [0.1, 1.3, 1]]
field = Field({'monopoles': m})
doc.draw_charges(field)
n = 64
k = 4
for i in range(n):
a = (0.5 + i) / n
a = 2.0 * pi * a
for j in range(k):
line = FieldLine(field, [m[j][0], m[j][1]],
start_v=[cos(a), sin(a)],
directions='forward')
doc.draw_line(line, arrows_style=None)
doc.write()
#!/usr/bin/python3
# Original source code by Wikimedia Commons user Geek3, GPL v3:
# https://commons.wikimedia.org/wiki/File:VFPt_sphere-magnets-parallel.svg
# Modified by B. Crowell.
import math
from math import *
from vectorfieldplot import FieldplotDocument, Field, FieldLine
import scipy as sc
# ... https://github.com/CD3/VectorFieldPlot
doc = FieldplotDocument('a', commons=True, width=800, height=600)
def spheremagnet_field(xy, p, xy0, R):
r = xy - xy0
d = math.sqrt(r[0]**2 + r[1]**2)
if d < R:
# inside the field is indeed constant
Fxy = p / (2. * pi * R**3)
else:
# outside the field is exatly that of a point-dipole
Fxy = (3. * sc.dot(p, r) * r - sc.dot(r, r) * p) / (4. * pi * d**5)
return Fxy
xy0 = sc.array([-1.5, 0.0])