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import sys
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
def E(q, r0, x, y):
"""Return the electric field vector E=(Ex,Ey) due to charge q at r0."""
den = np.hypot(x-r0[0], y-r0[1])**3
return q * (x - r0[0]) / den, q * (y - r0[1]) / den
# Grid of x, y points
nx, ny = 64, 64
x = np.linspace(-2, 2, nx)
y = np.linspace(-2, 2, ny)
X, Y = np.meshgrid(x, y)
# Create a multipole with nq charges of alternating sign, equally spaced
# on the unit circle.
nq = 2**int(sys.argv[1])
charges = []
for i in range(nq):
q = i%2 * 2 - 1
charges.append((q, (np.cos(2*np.pi*i/nq), np.sin(2*np.pi*i/nq))))
# Electric field vector, E=(Ex, Ey), as separate components
Ex, Ey = np.zeros((ny, nx)), np.zeros((ny, nx))
for charge in charges:
ex, ey = E(*charge, x=X, y=Y)
Ex += ex
Ey += ey
fig = plt.figure()
plt.rcParams['axes.facecolor'] = 'black'
ax = fig.add_subplot(111)
# Plot the streamlines with an appropriate colormap and arrow style
color = 2 * np.log(np.hypot(Ex, Ey))
ax.streamplot(x, y, Ex, Ey, color=color, linewidth=1, cmap=plt.cm.inferno,
density=2, arrowstyle='->', arrowsize=1.5)
# Add filled circles for the charges themselves
charge_colors = {True: '#aa0000', False: '#0000aa'}
for q, pos in charges:
ax.add_artist(Circle(pos, 0.05, color=charge_colors[q>0]))
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_xlim(-2,2)
ax.set_ylim(-2,2)
ax.set_aspect('equal')
plt.show()
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