Gauss

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 …

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Overview of Gauss’ Theorem and Basics of Integration

It turns out that deriving Gauss’ Law is easier said than done. There are several steps according to a StackExchange post [1]. The first of these steps is understanding Gauss’ Theorem. Hmm. Perhaps Gauss used his own theorem to derive his electrostatics law. After a quick online search, it is clear that Gauss’ Theorem is …

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Gauss’ Law, Part 1

In Derivation #3, the expression, $ \frac{\partial \beta(t)}{\partial t}$, was written. This is an expression for a derivative of a function $ \beta(t)$. Now that a derivative has been introduced, Maxwell’s equations can be investigated. I start with Gauss’ Law. But first, slightly more information about derivatives is needed. I can consider the pieces of …

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