who invented the inductor?

Answer 1

It was known long before that electrical current caused a magnetic field. Knowing how to determine the amount and direction (vector) of the magnetic field, however, was not yet known.

Joseph Henry was the first to actually coil wire and learn how to make the coiled wire control the direction that the needle of a magnetic compass pointed. So with that in mind, the answer is Joseph Henry.

Joseph Henry and Michael Faraday both discovered self-inductance right around the same time as each other but Henry published his findings on it earlier. Faraday, however, invented the transformer.