Editing Voltage (section)

=== Electrodynamics ===
{{Main articles|Electric potential#Generalization to electrodynamics}}
The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential.<ref name=":1" />{{Rp|417}} Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of [[Gauge fixing|gauge]].<ref group="note">For example, in the [[Lorenz gauge condition|Lorenz gauge]], the electric potential is a [[retarded potential]], which propagates at the [[speed of light]]; whereas in the [[Coulomb Gauge|Coulomb gauge]], the potential changes instantaneously when the source charge distribution changes.</ref><ref name=":1" />{{Rp|419-422}}

In this general case, some authors<ref>{{Cite book|last1=Moon|first1=Parry|url=https://books.google.com/books?id=lijEAgAAQBAJ&pg=PA126|title=Foundations of Electrodynamics|last2=Spencer|first2=Domina Eberle|publisher=Dover Publications|year=2013|isbn=978-0-486-49703-7|pages=126|access-date=2021-11-19|archive-date=2022-03-19|archive-url=https://web.archive.org/web/20220319091311/https://books.google.com/books?id=lijEAgAAQBAJ&pg=PA126|url-status=live}}</ref> use the word "voltage" to refer to the line integral of the electric field, rather than to differences in electric potential. In this case, the voltage rise along some path <math>\mathcal{P}</math> from <math>\mathbf{r}_A</math> to <math>\mathbf{r}_B</math> is given by:
:<math>\Delta V_{AB} = -\int_\mathcal{P} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell}
</math>
However, in this case the "voltage" between two points depends on the path taken.