While on Mivtzoyim, as I was taking off the Teffilin, it fell on the floor (carpet). What should I do?
The Alter Rebbe brings that a person should fast if the tefillin fell without a covering from the hand to the floor. If the tefillin were in their case at the time, there is no need to fast.
Since you are a yeshiva student, and need your koach for learning, you should fast half the day and redeem the remainder of the day with tzedakah (about seven or eight dollars). This would also apply to a Kollel yungerman or a teacher of kodesh subjects—and to anyone with health issues or a weak constitution. If even a half-day fast is difficult, you may give tzedakah for the cost of all meals in place of fasting.
Ideally, you should formally commit to your fast in Shemone Esrei of Mincha (at the end of Elokai Netzor) with the words “Hareni b’taanis l’machar ad chatzos.” (I hereby accept to fast tomorrow until noon.)
It would also be appropriate to undertake a hachlata (good resolution) in connection with the kedusha of tefillin, such as refraining to speak while wearing them, or an increase in learning the laws of tefillin and the maamarim connected to tefillin.
Shulchan Aruch Admor Hazaken (Orach Chayim 44:2). Chayim She’al (Chida) 1:12. Divrei Chayim end of Vol 2.
See also Sharei Halacha Uminhag Vol. 1 pages 72-73 (in connection to one who forgot to put on Rebeinu Tam).