In this paper we present frequency and transient analysis of a thin tabular conductive slab in lossy Earth due to a uniform magnetic line source excitation. The line source is parallel to the slab, and thus the problem is two dimensional. Under these conditions the frequency domain solution can be expressed in the form of a series which has an exact time domain representation. Our results are checked against two well-known limiting cases. This problem can model ore slabs and fluid-filled cracks in geophysical applications. The analytical and numerical results give a diagnosis of the thickness and conductivity of the slab and provide physical insight in the interpretation of actual field data.