Elektromagnetism
In the year 1820, the physicist Hans Christian Ørsted already observed that a compass needle is affected by a current-carrying wire closeby. Thus Ørsted discovered the magnetic effects of the electric current. (Compasses only react to magnetic fields.)
Within few years it was discovered that this effect is amplified when the wire is wound into a coil.
Straight Conductor
Today we know that a magnetic field forms in a circle around a current-carrying conductor. The formation of the magnetic field depends on the direction of the current and can be determined by the 'Left-Hand-Rule'. If we make a fist out of our left hand (as in the opposite image)and stick out our thumb into the direction of the current-flow (red), the other fingers point into the same direction as the electric field (blue).
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Coil
In coils, the magnetic fields of the individual curls overlap. Because opposite magnetic fields have opposite directions of rotation, their overlay on the inside points into the same direction.
Because of the overlap of the many small magnetic fields, on the whole, one strong magnetic field forms, which has a north and a south pole just like bar magnets.