Editing Gauss's Law (Electric): (section)

== Mathematical Formulation ==

=== Integral Form ===
<math>
\oint_{\text{closed surface}} \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}
</math>

Where:
* <math>\vec{E}</math> is the electric field vector,
* <math>d\vec{A}</math> is an infinitesimal area vector on the closed surface (pointing outward),
* <math>Q_{\text{enc}}</math> is the total electric charge enclosed within the surface,
* <math>\varepsilon_0</math> is the vacuum permittivity (<math>\varepsilon_0 \approx 8.854 \times 10^{-12}\, \text{C}^2/\text{N·m}^2</math>).

=== Differential Form ===
Using the divergence theorem, Gauss's Law can also be expressed in differential form:

<math>
\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}
</math>

Where:
* <math>\nabla \cdot \vec{E}</math> is the divergence of the electric field,
* <math>\rho</math> is the volume charge density (charge per unit volume).