Yes, it may simply be defective. I once bought a floppy drive that I returned for exchange; the second one worked. This happened to be a Sony.
If you could test that drive in another computer, that would give you confirmation before concluding that it's defective.
Have you had a floppy in your computer in the past? Another test would be to temporarily pull a working floppy from another computer and see if it will work in your computer.