The use of Helmholtz aiding coils to induce small electromagnetic (EM) fields in living tissue for both medical and research purposes has become quite common. While much progress has been made in showing that these induced EM signals can cause a variety of effects in tissues and individual cells, a satisfactory explanation of how the effects occur or how the EM signals couple to the tissue has not yet emerged. To address the latter problem adequately, it becomes necessary to know the spatial distribution of the induced fields inside a given set of boundaries. This paper examines the situation used for much in vitro research where a cylindrical culture dish is filled with a conducting solution and placed between the Helmholtz coils. Two cases are considered. The first assumes that the coils are above and below the culture dish (the planes of the coils are parallel with the top and bottom of the dish); the second assumes that the planes of the coils are parallel with the sides of the dish. A closed form solution is obtained for both cases, and it is shown that the induced EM field distribution is markedly different for the two cases.