= Solution
The integral and differential forms of <Gauss's law> in <electrostatics> are
$$
\boxed{\oint_{\partial\mathcal V}\mathbf E\cdot d\mathbf A
=\frac{Q_{\rm enc}}{\epsilon_0},\qquad
\nabla\cdot\mathbf E=\frac{\rho}{\epsilon_0}.}
$$
Here $\partial\mathcal V$ is a closed surface bounding a volume $\mathcal V$, $d\mathbf A=\hat{\mathbf n}\,dA$ is its outward area <vector>, $\mathbf E$ is the <electric field>, $\rho$ is total volume <charge density>, and $Q_{\rm enc}=\int_{\mathcal V}\rho\,d^3r$ is enclosed <electric charge>. The <divergence theorem> converts one form to the other. For ideal sheets or <point charges>, interpret the differential equation with their distributional <charge densities>.
Back to article page
