This paper describes a paradox in electromagnetic theory involving a charge moving with a velocity v parallel to a current carrying wire. In the frame of reference of the wire, the charge feels a magnetic force. In the frame of reference of the charge, there is no magnetic force, but there is an electric force due to the wire becoming charged. The charge on the wire can only be explained by length contractions from the theory of special relativity. This paradox is resolved both qualitatively and quantitatively.