Situation A positive test charge q is moving parallel to a current-carrying wire with velocity v relative to the wire in frame S. It is assumed that the net charge on the wire is zero and that the electrons in the wire also move with velocity v in a straight line. The leftward current in the wire produces a magnetic field that forms circles around the wire and is directed into the page at the location of the moving test charge. Therefore, a magnetic force directed away from the wire is exerted on the test charge. However, no electric force acts on the test charge because the net charge on the wire is zero when viewed in this frame. Now consider the same situation as viewed from another frame S', where the test charge is at rest. In this frame, the positive charges in the wire move to the left, the electrons in the wire are at rest, and the wire still carries a current. Because the test charge is not moving in this frame, there is no magnetic force exerted on the test charge when viewed in this frame. However, if a force is exerted on the test charge in frame S, the frame of the wire, as described earlier, a force must be exerted on it in any other frame. What is the origin of this force in frame S', the frame of the test charge? The answer to this question is provided by the special theory of relativity. A Possible Solution When the situation is viewed in frame S the positive charges are at rest and the electrons in the wire move to the right with a velocity v. Because of length contraction, the electrons appear to be closer together than their proper separation. Because there is no net charge on the wire this contracted separation must equal the separation between the stationary positive charges. The situation is quite different when viewed in frame S'. In this frame, the positive charges appear closer together because of length contraction, and the electrons in the wire are at rest with a separation that is greater than that viewed in frame S. Therefore, there is a net positive charge on the wire when viewed in frame S'. This net positive charge produces an electric field pointing away from the wire toward the test charge, and so the test charge experiences an electric force directed away from the wire. Thus, what was viewed as a magnetic field (and a corresponding magnetic force) in the frame of the wire transforms into an electric field (and a corresponding electric force) in the frame of the test charge. Problem How in the world is length contraction feasible? In Electric Current the electrons move with Drift Velocity.For ordinary currents, this drift velocity is on the order of millimeters per second in contrast to the speeds of the electrons themselves which are on the order of a million meters per second. At such low speeds the effect of length contraction would be negligible. How is relativity a possible solution to the above situation.