Potential due to a current source and sink -

L1.11a.py

import math

def distance(x=0,y=0,z=0) :
  return math.sqrt(x*x + y*y + z*z)

def monopole_potential(Io,sigma,r) :
  """ compute the potential in volts at a distance r from a monopole current source
  Io current in amp
  sigma  - conductivity in ohm-1 m-1
  r distance in m
  dimensionally  of the equation is amp / (ohm-1 m-1 m)  = amp ohm  = volt
  """

  return Io / (4 * math.pi * sigma *  r )


#  problem from Bioelectricity course Lecture 1 section 11
#  2 mA source and sink 1 mm apart in x direction
#  resistivity is 100.5 ohm-cm 
#  what is potential at distance 10 mm from one source in the z direction (y= 0)
#  using the MKS system
Io = 2E-3
r-source = 10E-3
d = 1E-3
r-sink = distance(d,0,r-source)

rho =  100.5 * 1.0E-2 # ohm-m
sigma = 1.0 / rho

phi-source = monopole_potential(Io,sigma,r-source)
phi-sink = monopole_potential(-Io,sigma,r-sink)
phi = phi-source + phi-sink
print r-source,r-sink,rho,phi-source,phi-sink,phi,"Volts"

See Lecture 1 section 11 on the Coursera Bioelectricity course https://www.coursera.org/course/bioelectricity