An electromagnetic solution for a thin tabular conductor in a lossy medium is presented. This is an extension of “Maxwell's theorem.” Both impulsive and time harmonic electric line sources are analyzed. The orientation of the source is parallel to the sheet conductor. This assumption renders the problem two-dimensional. The solution and associated analytical results have application to geophysical probing. For example, the sheet can model a conducting ore dyke or a fluid-filled crack in an induction logging application. Transient numerical results are seen to be diagnostic of the conductivity thickness product W = σ2d.