The time-dependent Maxwell equations without displacement current terms are solved above, within, and below a doubly infinite slab of finite conductivity and arbitrary thicknessDwith a prescribed current in an infinitely long wire above and parallel to the slab. Closed analytic expressions for the magnetic and electric field above the ground plane are obtained by transform methods in terms of a Laplace transform variable representing time. For finiteDthe results in actual time are computed by numerical inversion of the Laplace transform; forD = infinthey are given analytically to within numerical quadratures. Asymptotic expressions valid for large time and/or large lateral distance from the wire are obtained both forD < infinandD = infin. A summary of numerical results is given.