Too often, students in introductory courses are left with the impression that Einstein's special theory of relativity comes into play only when the relative speed of two objects is an appreciable fraction of the speed of light ("c"). In fact, relativistic length contraction, along with Coulomb's law, accounts quantitatively for the force on a charged particle as it moves relative to a current-carrying wire. That force, which in the reference frame of the wire we call "magnetic," is measurable and important even at relative speeds on the order of 10[superscript -12]c. This paper offers a straightforward way of introducing students to the connection between magnetism and special relativity and provides references to more in-depth treatments, especially those of E.R. Huggins and of E.M. Purcell as simplified by D.V. Schroeder.