One subtle point in our development is that (4) only
determines 
, it does not determine 
completely. For
instance we may add the curl of any vector field 
to our form,
without affecting (4) because 
for all vector fields 
. Fortunately, the freedom
involved in this choice has no physical consequences because when
integrating the flux over any closed surface, the term
has no effect, 
.
In writing (5) we did make a particular choice, however.
We made the conventional choice of the
consistent with (4) which
minimizes the total magnitude of the flow 
.
This minimization condition is equivalent to insisting 
.
A quick calculation (keeping
in mind that 
for any scalar field 
)
verifies that our form (5) meets this condition,
