In plane magnetic field of a current loop of radius a, distance r from the loop axis. Field will be perpendicular to the plane.

MagField2.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 z^2 + (r-a)^2
def epsilon_val (R, Z):
    epsilon = np.square(Z) + np.square(np.subtract(a, R))
    return epsilon

# equal to a^2 - z^2 - r^2
def delta_val (R, Z):
    delta = np.square(a) - np.square(Z) - np.square(R) 
    return delta



R = np.arange(0.0, 5, 0.01)
K = k_val(R, 0)
gamma = gamma_val (R, 0)
epsilon = epsilon_val (R, 0)
delta = delta_val (R, 0)

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

Bza = np.divide((mu * current) / (2 * np.pi), gamma)
Bzb = np.multiply(np.divide(delta, epsilon), E2) + E1

Bz = Bza * Bzb

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

ax.plot (R, Bz)

ax.set_ylim([-0.000003,0.000003])
plt.draw()
plt.show()