When two forward Qomar women have the doctor "trapped" in Sickbay, he calls for Security then deactivates himself. When he deactivates, his mobile emitter does indeed remain and visibly drop to floor.
When the Doctor is briefing Ensign Paris about the duties in Sick Bay, he says he'll be within com range for about a month. This is inaccurate because at the end of season 2 during "Resolutions" it's been established that Voyager can only remain within com range for 36 hours.