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Author: oonap0oo

electrical_field_2_charges.py

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+# Electrical field due to 2 point charges
+#
+# |
+# q1 o 
+# | + observation point
+# |
+# -----------------------------------------
+# |
+# |
+# q2 o
+# |
+#
+# rq1: vector to point charge 1
+# rq2: vector to point charge 2
+# ro: vector to observation point
+# r1o: vector from point charge 1 to observation point o
+# r2o: vector from point charge 2 to observation point o
+#
+# ro = rq1 + r1o
+# => r1o = ro - rq1
+# r2o = ro - rq2
+#
+# q1: charge value of point charge 1
+# q2: charge value of point charge 2
+# εo: permittivity of a vacuum,
+# 8.854 x 10⁻¹² F/m (Farads per meter)
+# E(ro): electric field at observation point ro
+#
+# Electrical field at ro:
+# E = 1/(4*pi*εo) * (r1o * q1 / |r1o|³ + r2o * q2 / |r2o|³) 
+#
+#
+# | x1o = xo - xq1
+# | y1o = yo - yq1
+#
+# | x2o = xo - xq2
+# | y2o = yo - yq2
+#
+# | Ex = 1/(4*pi*εo) * ( (xo - xq1) * q1 / |ro - rq1|³ + (xo - xq2) * q2 / |ro - rq2|³ ) 
+# | Ey = 1/(4*pi*εo) * ( (yo - yq1) * q1 / |ro - rq1|³ + (yo - yq2) * q2 / |ro - rq2|³ )
+#
+# Electrical potential
+# V = 1/(4*pi*εo) * ( q1 / r1o + q2 / r2o )
+# V = 1/(4*pi*εo) * ( q1 / (ro - rq1) + q2 / (ro - rq2) )
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+# parameters
+d = 0.01 # distance point charges from origin
+L = 2*d # distance between point charges
+q1 = 1; q2 = -1 # value point charges [coulomb]
+N = 20 # number of points calculated, result arrays will be N*N
+epsilon = 8.854E-12 # [F/m]
+#k = 1/(4 * np.pi * epsilon) # physical value
+k = 1 # used so E is scaled with 1/(4 * np.pi * epsilon)
+
+# preparing vectors with coordinates of point charges [x, y]
+rq1 = np.array([0, +d / 2]) 
+rq2 = np.array([0, -d / 2])
+
+# generate X and Y arrays
+x = np.linspace(-L, L, N)
+y = np.linspace(-L, L, N)
+X,Y = np.meshgrid(x,y)
+
+# prepare arrays for x and y components of E 
+Ex = np.zeros([N,N])
+Ey = np.zeros([N,N])
+
+# prepare array for V,V will be limted to Vmax
+V = np.zeros([N,N])
+Vmax = 100
+
+# function calculates x and y components of E
+# argument of function is vector ro with 2 coordinates
+# np.linalg.norm() gives the magnitude of the vector in this case
+def calc_E(ro):
+ Ex = k * ( (ro[0] - rq1[0]) * q1 / np.linalg.norm(ro - rq1)**3
+ + (ro[0] - rq2[0]) * q2 / np.linalg.norm(ro - rq2)**3 )
+ Ey = k * ( (ro[1] - rq1[1]) * q1 / np.linalg.norm(ro - rq1)**3
+ + (ro[1] - rq2[1]) * q2 / np.linalg.norm(ro - rq2)**3 )
+ return Ex, Ey
+
+# function calculates V
+# argument is vector ro with 2 coordinates
+def calc_V(ro):
+ Vt = k * ( q1 / np.linalg.norm(ro - rq1) + q2 / np.linalg.norm(ro - rq2) )
+ return Vt
+
+# calling calc_E() and calc_V() for each point
+for row in range(N):
+ for column in range(N):
+ ro = np.array([X[row,column], Y[row,column]])
+ Ex[row,column], Ey[row,column] = calc_E(ro)
+ V[row,column] = calc_V(ro)
+
+# calculating array containing magnitude of E
+E = np.sqrt(Ex**2 + Ey**2)
+
+# limiting V to +-Vmax to aid contour plot
+V = np.clip(V, -Vmax, Vmax)
+
+# plotting
+plt.rcParams.update({'font.size': 15})
+plt.figure(figsize=(11, 9))
+plt.quiver(X, Y, Ex/E, Ey/E)
+plt.contour(X, Y, V, levels = 15)
+plt.scatter(rq1[0], rq1[1], marker = "o", color = "red")
+plt.scatter(rq2[0], rq2[1], marker = "o", color = "blue")
+plt.title("Electric field / (1/(4*pi*εo)) [V/m]\nElectric potential [V]")
+plt.xlabel("E/(1/(4*pi*εo)) [V/M]\nV [V]")
+plt.ylabel("E/(1/(4*pi*εo)) [V/M]\nV [V]")
+plt.show()
+
+
+
+
+