When the current in a grounded wire is terminated abruptly, currents immediately flow in the Earth to preserve the magnetic field. Initially the current is concentrated near the wire, with a broad zone of return currents below. The electric field maximum broadens and moves downward with time. Currents are channeled into a conductive three-dimensional body, resulting in anomalous magnetic fields. At early times, when the return currents are channeled into the body, the vertical magnetic field is less than the half-space field on the far side of the body but is greater than the half-space field between the source and the body. Later the current in the body reverses; the vertical field is enhanced on the far side of the body and decreased between the source and the body. The horizontal magnetic field has a well-defined maximum directly over the body at late times, and is a better indicator of the position of the body.The vertical magnetic field and its time derivative change sign with time at receiver locations near the source if a three-dimensional body is present. These sign reversals present serious problems for one-dimensional inversion, because decay curves for a layered earth do not change sign. At positions away from the source, the decay curves exhibit no sign reversals--only decreases and enhancements relative to one-dimensional decay curves. In such cases one-dimensional inversions may provide useful information, but they are likely to result in fictitious layers and erroneous interpretations.