The mathematical parallels between electrostatics and laminar fluid flow are exploited to develop a set of problems that lead introductory physics students to discover Gauss’s law. The primary fluid experiment involves examining the flow between two closely spaced plates and the continuity equation in two dimensions. The extrapolation of the two-dimensional velocity field to three dimensions yields a radial dependence that is analogous to Coulomb’s law. This analogy allows the student to predict an electrical version of the continuity equation equivalent to Gauss’s law.
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