|How does running current through a coil cause a magnetic field?
Electricity and magnetism are interrelated in a great many ways. At the very basic levels, they are manifestations of the same fundamental physical concepts. As a result, electricity can produce magnetism and magnetism can produce electricity. One way in which electricity can produce magnetism is for charged particles to move. When an electric current passes through a coil (or any wire, for that matter), it creates a magnetic field. The coil develops a north magnetic pole and a south magnetic pole. I can't really explain why because the answer is simply that moving charges create magnetic fields; that's the way our universe works and no one has ever seen otherwise.