# derive-it.com

• ## Gauss’s Law in One Dimension and in Three Dimensions

Recall the following form of Gauss’s Law from this post: $\frac{\partial}{\partial x} E_x + \frac{\partial}{\partial y} E_y + \frac{\partial}{\partial z} E_z = \frac{\rho}{\epsilon_0 \epsilon_r}$ One Dimension If a problem is “one-dimensional” along the, say, $x$-axis, one has $\frac{\partial}{\partial x} E_x = \frac{\rho}{\epsilon_0 \epsilon_r}$ In words: the partial derivative with respect to $x$…

• ## Gauss’s Law in Differential Form and Cartesian Coordinates

Gauss’s Law in Differential Form In differential form, Gauss’s Law is $\vec{\nabla} \cdot \vec{E} = \frac{\rho}{\epsilon_0 \epsilon_r}$ The next part of this post attempts to demystify this law a bit. Description of Symbols The $\vec{\nabla}$ on the left is called ‘del’, and it can be written in terms of Cartesian unit vectors and…

• ## Short Overview of Special Relativity based on Zangwill

Here is a summary of Section 22.1 (Special Relativity) of Zangwill’s Electrodynamics textbook . Basic Points of Special Relativity There are different observers. One observer moves with a constant velocity with respect to the other observer. A velocity vector has a direction & a magnitude, so a constant velocity means that the moving observer’s direction &…

• ## The Electric Field

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