from __future__ import division
from __future__ import unicode_literals
from __future__ import print_function
from __future__ import absolute_import
from future import standard_library
standard_library.install_aliases()
from past.utils import old_div
import numpy as np
from scipy.constants import mu_0, pi
from scipy.special import erf

def hzAnalyticDipoleT(r, t, sigma):
    theta = np.sqrt(old_div((sigma*mu_0),(4*t)))
    tr = theta*r
    etr = erf(tr)
    t1 = (old_div(9,(2*tr**2)) - 1)*etr
    t2 = (old_div(1,np.sqrt(pi)))*(old_div(9,tr) + 4*tr)*np.exp(-tr**2)
    hz = old_div((t1 - t2),(4*pi*r**3))
    return hz