## The Electric Field

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

## 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 $\frac{\partial \beta(t)}{\partial t}$ 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