The Electric Field

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

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 $ \frac{\partial \beta(t)}{\partial t}$ separately. These pieces are $ \beta(t)$ and $ \frac{\partial}{\partial t}$. The $ \beta(t)$ is, of course, a function while $ \frac{\partial}{\partial t}$ is an operator called a differential operator that forms $ \frac{\partial \beta(t)}{\partial t}$ if $ \frac{\partial}{\partial t}$ is

Gauss’ Law, Part 1Read More »