Editing Voltage (section)

=== Electrostatics ===
[[File:Opfindelsernes bog3 fig282.png|thumb|The electric field around the rod exerts a force on the charged pith ball, in an [[electroscope]]]]
[[File:Electrostatic definition of voltage.svg|thumb|In a static field, the work is independent of the path]]

{{Main articles|Electric potential#Electrostatics}}
In [[electrostatics]], the voltage increase from point <math>\mathbf{r}_A</math> to some point <math>\mathbf{r}_B</math> is given by the change in [[Electric potential#Electrostatics|electrostatic potential]] <math display="inline">V</math> from <math>\mathbf{r}_A</math> to <math>\mathbf{r}_B</math>. By definition,<ref name=":1">{{Cite book|last=Griffiths|first=David J.|title=Introduction to Electrodynamics|publisher=Prentice Hall|year=1999|isbn=013805326X|edition=3rd|pages=}}</ref>{{Rp|78}} this is:

:<math>\begin{align}
\Delta V_{AB} &= V(\mathbf{r}_B) - V(\mathbf{r}_A) \\
&= -\int_{\mathbf{r}_0}^{\mathbf{r}_B} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} - \left(-\int_{\mathbf{r}_0}^{\mathbf{r}_A} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} \right)\\
&= -\int_{\mathbf{r}_A}^{\mathbf{r}_B} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell}
\end{align} </math>

where <math>\mathbf{E}</math> is the intensity of the electric field.

In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration.<ref name=":1" />{{Rp|90-91}} Mathematically, this is expressed as the [[line integral]] of the [[electric field]] along that path. In electrostatics, this line integral is independent of the path taken.<ref name=":1" />{{Rp|91}}

Under this definition, any circuit where there are time-varying magnetic fields, such as [[Alternating current|AC circuits]], will not have a well-defined voltage between nodes in the circuit, since the electric force is not a [[conservative force]] in those cases.<ref group="note" name=":0">This follows from the [[Maxwell-Faraday equation]]:

<math>\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}</math>

If there are changing magnetic fields in some [[Simply connected space|simply connected]] region, then the [[Curl (mathematics)|curl]] of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, see {{Section link|Conservative force|Mathematical description}}.</ref> However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see [[Electrostatics#Electrostatic approximation|electrostatic approximation]]).