• 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 $x$…