## The Electric Field

In this post, an expression for the electric field is derived.

## Proof of Gauss’ Theorem for a Rectangular Prism

Recall Gauss’ theorem, $\int\int\int_V (\vec{\nabla} \cdot \vec{F}) dV = \int\int_{S} (\vec{F} \cdot \vec{e}_{n}) dS$. This theorem can be written more precisely. The following statement of the Divergence theorem is a copy from reference [1]. Definitions are provided first. Volume $V$: Define $V$ as a region comprising three spatial dimensions. The volume has no holes in it. Boundary $\partial V$: Define $\partial V$ as a once-differentiable surface surrounding the volume $V$. The boundary has a thickness of zero and no holes in it. Points not in $V$ are not in $\partial V,$