In conformity with what the author (1949a) presented briefly, the theory is developed of the electromagnetic eddy fields relative to a plane, thin, conducting slab with its plane perpendicular to the horizontal ground. The mineral slab is subjected to an alternating inducing magnetic field, paralleling the surface of the ground. After discussing the problem of the finite slab, the special case is considered of a semi-infinite slab (Peters and Bardeen, 1930), e.g., the mineralized vein type, using existing formulas. With adequate development they can be used in the construction of theoretical graphs of the electromagnetic effects of the slab in which eddy currents are produced.The limiting dimensions, both of the dyke (first case of the finite slab), and the vein (second of the semi-infinite slab case), act noticeably upon the measurable electromagnetic effect, and the influence diagrams characterize the slab-shaped, conducting mineral. Therefore some fundamental characteristics on the surface and at depth of the slab and its extension in depth (thickness) can be deduced.The present paper consists of two sections, namely, (A) The theory of the finite, plane, and thin slab (dyke) and corresponding general formulas of magnetic influence. (B) A discussion of the special case of the semi-infinite slab, or mineralized vein and of Peters-Bardeen's (1930) integral formulas, and their integration and illustration by means of graphs.