
344 Forensic Engineering Fundamentals
e charge density can be described as such:
ρ
σ
µ
=
(11.8)
μ is the mobility of charged particles
σ is the conductivity = 0.01 V/m
Conduction can be varied to depict various sources for freshwater.
erefore, K = 0.014 V/m
2
for freshwater.
Poisson’s equation is a nonhomogeneous partial dierential equation (PDE) with non-
homogeneous boundary conditions. erefore, we separate it into
1. Steady-state PDE (K = 0) with nonhomogeneous boundary conditions
2. e given PDE (∇
2
V = −K) with homogenous boundary conditions steady-state PDE
∇=
∂
∂
+
∂
∂
=
2
2
2
2
2
0U
U
x
U
y
(11.9)
Boundary conditions:
Ux fx UxLgx(0)(), ()(),,==