As an integrative and insightful example for undergraduates learning about electrostatics, we discuss how to use symmetry, Coulomb's law, superposition, Gauss's law, and visualization to understand the electric field produced by a uniformly charged cubic shell. We first discuss how to deduce qualitatively, using freshman-level physics, the perhaps surprising fact that the interior electric field is nonzero and has a complex structure, pointing inwards from the middle of each face of the shell and pointing outwards towards each edge and corner. We then discuss how to understand the quantitative features of the electric field by plotting an analytical expression for E along symmetry lines and on symmetry surfaces of the shell.
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2018
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