The electric field of a uniformly charged cubic shell

Abstract

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 E(x, y, z) produced by a non-conducting cubic surface that is covered with a uniform surface charge density. We first discuss how to deduce qualitatively, using only elementary physics, the surprising fact that the electric field inside the cubic surface is nonzero and has a complex structure, pointing inwards towards the cube center from the midface of each cube 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. This example would be a good choice for group problem solving in a recitation or flipped classroom.

Electrostatic field of angular-dependent surface electrodes

“…However, obtaining an exact solution can be difficult depending on the charge density's distribution in space. In principle, it is possible to find analytic solutions to this problem in very different settings [1][2][3][4][5]. A particular case has to do with a fixed but not uniform potential distribution over a boundary surface.…”

Evidence of alloy formation in CoNi nanoparticles synthesized by nanosecond‐pulsed discharges in liquid nitrogen

“…Nickel cubes are prone to be equally attracted by the fluctuating plasma potential—as it oscillates in the RF range as the current flow—contrary to the predominantly spherical cobalt nanoparticles. [ 36 ]…”

Equipotential Surfaces for Uniformly Charged Symmetric Polyhedral Conductors

“…In previous research papers [1] the concept of the curvature of equipotential surfaces at sharp bends for cubical conductor has been discussed. No theory regarding the equipotential surface of other polyhedral conductors has been proposed.…”