• 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 [1]. 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.