1 Answer
The formula of Gauss's Law in vector form is:
\[
\oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}
\]
Where:
In simple terms, Gauss's Law states that the electric flux through a closed surface is proportional to the charge enclosed within the surface.
\[
\oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}
\]
Where:
- \(\oint_S\) represents the surface integral over a closed surface \(S\).
- \(\mathbf{E}\) is the electric field vector at a point on the surface.
- \(d\mathbf{A}\) is the differential area vector on the surface \(S\), which points outward and has a magnitude equal to the area of the differential element.
- \(Q_{\text{enc}}\) is the total charge enclosed by the surface \(S\).
- \(\varepsilon_0\) is the permittivity of free space (a constant), approximately equal to \(8.854 \times 10^{-12} \, \text{F/m}\).
In simple terms, Gauss's Law states that the electric flux through a closed surface is proportional to the charge enclosed within the surface.