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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 $x$…