Month: November 2020

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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Finite Differences

Here are a few notes about the symbol $ \Delta$. This symbol appears frequently in physics. Let $ \alpha$ be a real number. This statement is equivalent to $ \alpha \in \mathbb{R}$. Then $ \Delta \alpha$ can be defined as follows. Definition 1 Define a finite difference as $ \Delta \alpha \equiv \alpha_2 – \alpha_1$. …

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The Lorentz Transformation

This is an attempt to clarify the brief derivation of the Lorentz transformation in Albert Einstein’s book [1]. Suppose that the speed of light, $ c$, is the same regardless of whether a coordinate system is or is not translating with a nonzero speed.Next consider two coordinates systems.The first is called $ K$ and the …

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