Graphical analysis for a particle's attraction to a wire. (Based on Kellogg's: Foundation Of Potential Theory, Ch.1-S.4)

force_on_wire.py

import numpy as np
import matplotlib.pyplot as plt

# Set wire, plot lenght and p position:
p = 6   # P position, along x axis
l = 5   # Wire's length
wire = np.linspace(0, l, 2) # Wire's discretization
lmbd = 1    # Lamnbda value

# Plotting domain:
if p > l:
    x = np.linspace(-1, p+1, p+2*100)
else:
    x = np.linspace(-1, p+1, l+1*100)

# Force function evaluated on domain x:
Fx = -lmbd*l / (x*(x-l))

# Plot figure:
fig = plt.figure()
ax = fig.add_subplot(111)
plt.title('Straight homogeneous segment')

# Auxiliar axis:
plt.axvline(x=l/2, ymin=-1000, ymax = 1000, linewidth=0.5, color='k')
plt.axvline(x=l, ymin=-1000, ymax = 1000, linewidth=0.5, color='k')
plt.axvline(x=0, ymin=-1000, ymax = 1000, linewidth=0.5, color='k')
plt.axhline(y=0, xmin=-1000, xmax = 1000, linewidth=0.5, color='k')

# Main plots (wire, function, p):
w_plot, = plt.plot(wire, wire*0, '-g', label="Wire", linewidth=2)
g_plot, = plt.plot(x, Fx, '-b', label="F(x)", linewidth=1)
p_plot, = plt.plot(p, 0, 'or', label="P")
plt.legend(handles=[w_plot, p_plot, g_plot])
plt.show()