As already mentioned the black cable is an earth, there is normally 2 black wires on this alternator, one goes into the wiring loom which becomes the earth return for the engine sensors and controlling relays. The other black cable is just a short one earthing the unit itself to the engine block. Is the connector on the end of the loose cable a female part of a spade terminal? If the answer is yes then look for a threaded stud (about 4mm diameter)on the back of the alternator that should have the male part of the spade terminal on it, chances are that the terminal has been broken off from it and is still inside the wire connector - thats what happened on mine! have a look and see. I hope this is of some help.