<< While I'm railing against these neosacred cows, let me also deplore
the use of the word "potential (meaning electrical potential) in this or
any other time dependent application. I like to firmly associate the
terms "potential" and "time invariant" with one another. Perhaps "emf"
would be a better choice? >>
Perhaps so. However, Kirchhoff's loop rule -- that the sum of the
potential differences around a loop equals zero -- is a statement about
potential differences, not emfs/voltages. It seems to me this is
equivalent to stating that an irrotational (curl free) electric field
exists in the region. For an inductor, the net electric field has both
an irrotational (curl free)** part and a rotational part. Emf is
determined only by the rotational part whereas potential difference is
determined only by the irrotational part. Within the wire of an
induction coil it is the component of the *net* electric field tangent
to the wire's axis that equals rho*J, where rho is the resistivity and J
is the current density. If either the current density or the
resistivity are zero, the tangential component of the *net* electric
field also equals zero. The instantaneous potential difference V across
the coil is the negative of the integral of E_*dL along the axis of the
coil wire, from one end to the other, where E_ is the irrotational part
of the electric field. This integral is calculated for a single instant
in time. It follows that
V = E - Ir = -LdI/dt - Ir.
where E is the emf.
It seems to me that not only is it OK, it is desirable to refer to the
potential difference across a coil. Kirchhoff's loop rule is about
potential differences, not emfs.
** The source of the irrotational part of the electric field in an
inductor is the charges on the surface of the coil wire.