Editing Electric charge (section)

== Conservation of electric charge ==
<!-- This section is linked from Conservation law (physics) -->
{{Main|Charge conservation}}
The total electric charge of an [[isolated system]] remains constant regardless of changes within the system itself.<ref>{{Cite book |last=Purcell |first=E. M. |title=Berkeley Physics Course: Electricity and magnetism. |date=1963 |publisher=McGraw Hill |location=United States}}</ref> {{rp|4}}This law is inherent to all processes known to physics and can be derived in a local form from [[gauge invariance]] of the [[wave function]]. The conservation of charge results in the charge-current [[continuity equation]]. More generally, the rate of change in [[charge density]] ''ρ'' within a volume of integration ''V'' is equal to the area integral over the [[current density]] '''J''' through the closed surface ''S'' = ∂''V'', which is in turn equal to the net [[electric current|current]] ''I'':
: {{oiint|preintegral=<math>- \frac{d}{dt} \int_V \rho \, \mathrm{d}V = </math>|intsubscpt=<math>\scriptstyle \partial V</math>|integrand=<math>\mathbf J \cdot\mathrm{d}\mathbf S = \int J \mathrm{d}S \cos\theta = I.</math>}}

Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:
: <math>I = -\frac{\mathrm{d}q}{\mathrm{d}t}.</math>

The charge transferred between times <math>t_\mathrm{i}</math> and <math>t_\mathrm{f}</math> is obtained by integrating both sides:
: <math>q = \int_{t_{\mathrm{i}}}^{t_{\mathrm{f}}} I\, \mathrm{d}t </math>
where ''I'' is the net outward current through a closed surface and ''q'' is the electric charge contained within the volume defined by the surface.