Name of a story about a Doctor's bag of surgical instruments transported back in time to the present day

Question

A bag of surgical instruments is transported back in time where it is found in the present by a person with limited medical experience who begins to use the instruments to perform miraculous cures on hopeless cases. He begins to acquire fame for his surgical skills but he is denounced by the medical community as a quack. In an effort to demonstrate to a conference of doctors his legitimacy, he performs a procedure upon himself where he will slit his own throat without harm. At the moment he begins his demonstration the bag is "switched off" and he ends up committing suicide.

It may have been published in OMNI in the 70's

Answer 1

This is "The Little Black Bag" by Cyril M. Kornbluth. You can read the full story here.

For the record, it was never published in Omni, but you may have read it in Astounding Science Fiction.

A "physicist" goads his minder into giving him specifications for a time machine. The faux physicist builds it, and uses it to send a "doctor" friend's highly automated medical kit into the past (our present), where it is found by Dr. Full, a physician who has succumbed to alcoholism and fallen to the bottom level of society. At first attributing its advanced properties and unfamiliar components to medical advances made since he last practiced, he uses it to heal a seriously injured young child. The patient's cynical eighteen-year-old sister, Angie, discovers the patent application date on one of the instruments (2450) and is quick to grasp the financial opportunities. She blackmails Full into taking her on as a partner.

...

Her first patient sees the sharp instruments and balks at another treatment. To reassure her, Angie demonstrates their safety by running a scalpel through her arm without harm. Still unconvinced, the client requests another test. Back in the future, a technician notes the bag has been used for murder and deactivates its advanced functions. Angie runs what has just become an ordinary scalpel across her own throat, with fatal results.

It might interest you to know that this story has been adapted for TV at least twice

and

"Night Gallery" The Little Black Bag