,The Capacitance Gradient
Starting with the Coulomb gauge potential of
the electric field for a single electron of charge ,
(11)
The potential of an electric field is its
voltage. The energy of the electric field is stored in a
capacitance 
. A capacitor is simply described as a thin tube of
electric flux in which the energy of the field is stored.
Parallel tubes of flux effectively form parallel capacitors
called guard capacitors, so there is no leakage from the
tube. No conductors are required in order to have capacitance, as
the electromagnetic field does not require a medium in which to
store energy.
The electric field is the gradient of the potential,
(12)
A change in the radial coordinate position is
equivalent to a change in the capacitance. The reciprocal of
capacitance is the elastance 
. If the charge
is held constant then the gradient of the capacitance is a
constant vector,
(13)
This can be written more compactly as a four-vector. Introducing the Minkowski metric tensor,
(14)
In this paper lower case Greek alphabet characters as superscripts represent contravariant four-vectors, and as subscripts represent covariant four-vectors. Indices are raised and lowered using the metric tensor. Three-vectors are shown with an arrow to indicate their three dimensional vector nature.
As a four-vector the capacitance gradient at
the space-time point 
is,
(15)
Capacitance is thus shown to be an effective
potential who’s gradient leads to a constant ratio of
capacitance per unit length, represented by a permittivity vector
. A
function of the constant of permittivity and a geometrical
variable.