The Electric Field

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

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,$

Proof of Gauss’ Theorem for a Rectangular PrismRead More »