Gauss's Law in differential form is expressed as \(\nabla \cdot \vec{E}(\vec{r}) = \rho(\vec{r})/\epsilon_0\), indicating that the electric field \(\vec{E}\) and charge density \(\rho\) are functions of position. The omission of the position variable is common but understood in context. Applying the divergence theorem allows for the derivation of Gauss's integral law, confirming the relationship between the differential and integral forms of Gauss's Law.
PREREQUISITESStudents of physics, particularly those studying electromagnetism, as well as educators and professionals seeking to deepen their understanding of Gauss's Law and its applications in various contexts.