The surprising subtlety of electrostatic field lines
arXiv:2411.08283 · doi:10.1119/5.0207201
Abstract
Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in electrostatics, from its field lines alone? Second, are there conservative electric fields with straight field lines, besides the familiar textbook examples with spherical, cylindrical, or planar symmetry? We give a self-contained introduction to the differential geometry required to answer these questions, assuming only vector calculus background.
8 pages, 4 figures; to appear in the American Journal of Physics