Answer to Question #7200 in Electromagnetism for Surnamed
Why does electrical current create magnetic field?
The detailed answer is pretty complex and involvs the Special Theory of Relativity. The principle is that a magnetic field is a result of the electric field of moving charges.
It's to do with relative motion. A magnetic field is what is experienced as a result of relative movement through an electric field. If you could move through an electric field at the speed of light (which you can't) you would experience no electric field, only a magnetic field.
Whenever there are charges moving relative to an observer, there is relative motion of the electric field between the observer and field, and a magnetic field is perceived. A magnetic filed can always be traced back to the electric field of moving charges.
In a wire, it is the motion of the moving charges which creates the magnetic field. The electrons move one way but the positive (atomic ion) charges stay fixed. The magnetic field is the effect of the moving electric field from the electrons. (Of course if you moved along with the electrons, the positive charges in the wire would now be moving in the opposite direction relative to you and you would experience the same field, but now produced by the moving field from the positive charges).