A current-carrying conductor generates a magnetic field, but if an object moves at the same speed as the current, the magnetic field's effects differ based on the observer's frame of reference. In the frame of the object moving with the current, there is no magnetic field present, although the electric field will vary compared to other frames. The relationship between electric and magnetic fields is described by Lorentz transformations, indicating that observers in relative motion will perceive different magnetic fields. The discussion highlights that current is not inherently linked to speed, but rather to the drift speed of electrons in the conductor. Understanding these concepts is crucial for analyzing electromagnetic phenomena.