Magnetic Resonance Imaging information depends on the knowledge of the behavior of the transverse, radio frequency (RF) electromagnetic fields inside biological objects. Here we present exact results for the RF vector potential field inside and outside a cylindrical object that minics the human body. These results are obtained by solving Maxwell Equations with appropriate boundary conditions, and take into consideration the object conductivity and dielectric constant and the presence of a cylindrical RF uniform-current-carrying coil. A computer code that evaluates RF magnetic field phase and magnitude is presented for two cases of interest: for a longitudinal and for a φ-directed current. Each of those cases is studied in free space and in the presence of a metallic shielding. The symbolic code will be of use for order-of-magnitude calculations in the clinical world and, for pedagogical uses in medical imaging courses.