A quick demonstration of the magnetic field of a circular current loop

MagField.py

import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp

a = 1.55
current = 1
mu = 4 * np.pi / 10000000

# equal to sqrt(4ra(z^2 + (a+r)^2)^(-1))
def k_val (R, Z):
    denominator = np.square(Z) + np.square(np.add(a, R))
    K = np.sqrt(np.divide(4 * R * a, denominator))
    return K

# equal to sqrt(z^2 + (a+r)^2)
def gamma_val (R, Z):
    gamma = np.sqrt(np.square(Z) + np.square(np.add(a, R)))
    return gamma

# equal to sqrt(z^2 + (r-a)^2)
def epsilon_val (R, Z):
    epsilon = np.square(Z) + np.square(np.subtract(a, R))
    return epsilon


R, Z = np.meshgrid(np.arange(0.1, 3, 0.1), np.arange(-3, 3, 0.1))
K = k_val(R, Z)
gamma = gamma_val (R, Z)
epsilon = epsilon_val (R, Z)

E1 = sp.ellipk(np.square(K))
E2 = sp.ellipe(np.square(K))

Ua = np.divide((mu * current) / (2 * np.pi), gamma)
Va = np.multiply(np.divide(np.divide((mu * current) / (2 * np.pi), gamma), R), Z)

U = np.multiply(
        Ua,
        np.add(
            np.multiply(
                np.divide(
                    (np.square(a) - np.square(Z) - np.square(R)),
                    epsilon),
                E2),
            E1))

V = np.multiply(
	    Va,
	    np.subtract(
            np.multiply(
                np.divide(
                    (np.square(a) + np.square(Z) + np.square(R)),
                    epsilon),
                E2),
            E1))


plt.figure(1)
ax =plt.gca()


mag = np.sqrt(V**2 + U**2)

Us = np.divide(U, mag)
Vs = np.divide(V, mag)

ax.quiver(R, Z, Vs, Us, angles='xy', scale_units='xy', scale=10 )
ax.set_xlim([0,3])
ax.set_ylim([-3,3])
plt.draw()


plt.figure(2)
ax = plt.gca()

ax.plot (Z[:,10], U[:,10])
ax.plot (Z[:,20], U[:,20])

ax.set_xlim([-3,3])
ax.set_ylim([-0.0000003,0.0000003])
plt.draw()
plt.show()