Electric fields produced by coplanar point charges have often been represented by field line diagrams that depict two-dimensional slices of the three-dimensional field. Serious problems with these "conventional" field line diagrams (CFLDs) have been overlooked. Two of these problems, "equatorial clumping" and "false monopole moment," occur because a two-dimensional slice lacks information vital to the accurate representation of an inherently three-dimensional field. Equatorial clumping causes most CFLDs to exhibit unphysical behavior such as irregular spacing between field lines terminating on negative charges. CFLDs can also mistakely indicate that a neutral charge distribution has a significant monopole moment. Such phenomena make the visual estimation of local field strength impossible and render CFLDs of little utility for representing three-dimensional fields. While these "projection" problems can be avoided by using two-dimensional field line diagrams to represent two-dimensional (1/r) electric fields, or by using three-dimensional field line diagrams to represent three-dimensional fields, other forms of distortion generally remain.