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()
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:
charge.plot()
finalize_plot()
pyplot.show()
XOFFSET = 0
electrostatics.init(XMIN, XMAX, YMIN, YMAX, ZOOM, XOFFSET)
# Set up the charges and electric field. The point with charge 0 is a
# termination point (0 electric field).
charges = [PointChargeFlatland(1, [-1, 0]),
PointChargeFlatland(-1, [1, 0])]
field = ElectricField(charges)
# Set up the Gaussian surface
g = GaussianCircle(charges[0].x, 0.1)
# Create the field lines
fieldlines = []
for x in g.fluxpoints(field, 12):
fieldlines.append(field.line(x))
fieldlines.append(field.line([3, 0]))
fieldlines.append(field.line([5, 0]))
# Plotting
fig = pyplot.figure(figsize=(6, 4.5))
field.plot(-1.7, 0.8)
for fieldline in fieldlines:
fieldline.plot()
for charge in charges:
charge.plot()
finalize_plot()
#fig.savefig('dipole-flatland.pdf', transparent=True)
pyplot.show()
