def test_monopole_fluxpoints(self):
"""Tests monopole flux points."""
field = ElectricField([PointCharge(2, [0, 0])])
circle = GaussianCircle([0, 0], 10)
fluxpoints = circle.fluxpoints(field, 4)
self.assertEqual(len(fluxpoints), 4)
self.assertTrue(
isclose(fluxpoints, [[10, 0], [0, 10], [-10, 0], [0, -10]]).all())
fluxpoints = circle.fluxpoints(field, 14)
self.assertEqual(len(fluxpoints), 14)
self.assertTrue(isclose(fluxpoints[0], [10, 0]).all())
self.assertTrue(isclose(fluxpoints[7], [-10, 0]).all())
x1 = fluxpoints[1:7]
x2 = fluxpoints[-1:7:-1]
x2[:, 1] = fabs(x2[:, 1])
self.assertTrue(isclose(x1, x2).all())
x1 = append(fluxpoints[-3:], fluxpoints[:4], axis=0)
x2 = fluxpoints[-4:3:-1]
x2[:, 0] = fabs(x2[:, 0])
self.assertEqual(len(x1), len(x2))
self.assertTrue(isclose(x1, x2).all())
def test_dipole_fluxpoints(self):
"""Tests dipole flux points."""
field = ElectricField(
[PointCharge(-2, [0, 0]),
PointCharge(2, [2, 0])])
circle = GaussianCircle([0, 0], 0.1)
fluxpoints = circle.fluxpoints(field, 4)
self.assertEqual(len(fluxpoints), 4)
fluxpoints = circle.fluxpoints(field, 14)
self.assertEqual(len(fluxpoints), 14)
self.assertTrue(isclose(fluxpoints[0], [0.1, 0]).all())
self.assertTrue(isclose(fluxpoints[7], [-0.1, 0]).all())
x1 = fluxpoints[1:7]
x2 = fluxpoints[-1:7:-1]
x2[:, 1] = fabs(x2[:, 1])
self.assertTrue(isclose(x1, x2).all())
from electrostatics import GaussianCircle, ElectricField
from electrostatics import finalize_plot
# pylint: disable=invalid-name
XMIN, XMAX = -40, 40
YMIN, YMAX = -30, 30
ZOOM = 6
XOFFSET = 0
electrostatics.init(XMIN, XMAX, YMIN, YMAX, ZOOM, XOFFSET)
# Set up the charges and electric field
a = 2
charges = [LineCharge(1, [0, -a], [0, a])]
field = ElectricField(charges)
# Set up the Gaussian surface
g = GaussianCircle([0, 0], 29)
# Create the field lines
fieldlines = []
for x in g.fluxpoints(field, 12):
fieldlines.append(field.line(x))
# Plotting
pyplot.figure(figsize=(6, 4.5))
field.plot()
for fieldline in fieldlines:
fieldline.plot()
for charge in charges:
def draw_E_and_V(charges,
locations,
background=False,
circlesize=True,
lines=True):
XMIN, XMAX = -40, 40
YMIN, YMAX = -40, 40
ZOOM = 5
XOFFSET = 0
electrostatics.init(XMIN, XMAX, YMIN, YMAX, ZOOM, XOFFSET)
# Set up the charges, electric field, and potential
charges = [
PointCharge(charges[i] * 1e9, locations[i][:2])
for i in range(len(charges))
]
field = ElectricField(charges)
potential = Potential(charges)
# Set up the Gaussian surface
fieldlines = []
for charge in charges:
g = GaussianCircle(charge.x, 0.1)
# Create the field lines
for x in g.fluxpoints(field, 12):
fieldlines.append(field.line(x))
fieldlines.append(field.line([10, 0]))
# Create the vector grid
x, y = numpy.meshgrid(
numpy.linspace(XMIN / ZOOM + XOFFSET, XMAX / ZOOM + XOFFSET, 41),
numpy.linspace(YMIN / ZOOM, YMAX / ZOOM, 31))
u, v = numpy.zeros_like(x), numpy.zeros_like(y)
n, m = x.shape
for i in range(n):
for j in range(m):
if any(
numpy.isclose(
electrostatics.norm(charge.x - [x[i, j], y[i, j]]), 0)
for charge in charges):
u[i, j] = v[i, j] = None
else:
mag = field.magnitude([x[i, j], y[i, j]])**(1 / 5)
a = field.angle([x[i, j], y[i, j]])
u[i, j], v[i, j] = mag * numpy.cos(a), mag * numpy.sin(a)
## Plotting ##
# Electric field lines and potential contours
fig = pyplot.figure(figsize=(20, 9))
pyplot.subplot(1, 2, 1)
#fig = pyplot.figure(figsize=(8, 6))
potential.plot()
potential.plot_color()
if background:
field.plot()
if lines:
for fieldline in fieldlines:
fieldline.plot()
for charge in charges:
charge.plot(circlesize)
finalize_plot()
#fig.savefig('dipole-field-lines.pdf', transparent=True)
# Field vectors
pyplot.subplot(1, 2, 2)
#fig = pyplot.figure(figsize=(8,6))
cmap = pyplot.cm.get_cmap('hsv')
pyplot.quiver(x, y, u, v, pivot='mid', cmap=cmap, scale=35)
for charge in charges:
charge.plot()
finalize_plot()
#fig.savefig('dipole-field-vectors.pdf', transparent=True)
pyplot.show()
def setUp(self):
"""Sets up a dipole centred at (0, 0)."""
charges = [PointCharge(-2, [-1, 0]), PointCharge(2, [1, 0])]
self.field = ElectricField(charges)
