CODEWITHSUNDEEP
pythonpython-3.xmatplotlibplotwolfram-mathematica
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Reputation: 41

Attempting to Create Vector Field Plot of Dipole using Matplotlib

I have been a long-time Mathematica user and I've been in the process of converting various notebooks into python (version 3). For plotting, I've been using matplotlib. I've ran into a snag and I am not sure what's going wrong.

I'm trying to convert the following Mathematica code:

(* simple electric dipole *)
Ex[x_, y_] := (x + 1)/((x + 1)^2 + y^2) - (x - 1)/((x - 1)^2 + y^2)
Ey[x_, y_] := y/((x + 1)^2 + y^2) - y/((x - 1)^2 + y^2)
StreamPlot[{Ex[x, y], Ey[x, y]}, {x, -3.5, 3.5}, {y, -3.5, 3.5}]

This produces the following figure:

Electric Dipole

I want to reproduce this using Python code.

from pylab import *
X,Y = meshgrid( arange(-4,4,.2),arange(-4,4,.2) )
Ex = (X + 1)/((X+1)**2 + Y**2) - (X - 1)/((X-1)**2 + Y**2)
Ey = Y/((X+1)**2 + Y**2) - Y/((X-1)**2 + Y**2)
figure()
Q = quiver( Ex, Ey)
l,r,b,t = axis()
dx, dy = r-l, t-b 
axis([l-0.05*dx, r+0.05*dx, b-0.05*dy, t+0.05*dy])
show()

Produces the following figure:

FUBAR

I'm still learning how to do plotting in python, and I'm a little unsure of how to create a vector field plot. Any insight would be appreciated.

Upvotes: 1

Views: 5989

Answers (1)

Austin Downey
Austin Downey

Reputation: 1055

This issue is that you have a very high intensity in your field at the nodes, so quiver scales it poorly. If we scale quiver with the argument scale=50 we get the plot:

enter image description here

However, if we use the streamplot function also in the pyplot we can get the following:

enter image description here

A much better plot if you ask me.

Here is the code for reference. 

import numpy as np
import matplotlib.pyplot as plt

#%% Plot the fields
X,Y = np.meshgrid( np.arange(-4,4,.2), np.arange(-4,4,.2) )
Ex = (X + 1)/((X+1)**2 + Y**2) - (X - 1)/((X-1)**2 + Y**2)
Ey = Y/((X+1)**2 + Y**2) - Y/((X-1)**2 + Y**2)

plt.figure()
plt.streamplot(X,Y,Ex,Ey)
plt.title('streamplot')

plt.figure()
plt.quiver(X,Y,Ex,Ey,scale=50)
plt.title('quiver')

Upvotes: 2

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