Once you've finished the College of Winterhold main quest, Tolfdir will give you the 'Aftershock' Radiant quest.
Before giving the quest for the first time, Tolfdir will say something along the lines of "I hope you still have the Staff of Magnus, you may (or will) need it."
However, I have tried completing this Radiant quest multiple times without using the Staff of Magnus at all (I just used a sword to kill the Magic Anomalies – they are tough and hard to hit).
My question is: Will the Staff of Magnus make completion of the 'Aftershock' Radiant quests easier or faster? Does it have a special function similar to its function in the last College of Winterhold main quest?
Related question: Do you need the Staff of Magnus after killing Arcano?
Best Answer
The odds are pointing towards no. On the Quest Stages page, it doesn't mention anything about the Staff of Magnus being used for anything (besides his recommendation,) just the Eye. If it really was crucial, it would have been listed on the Quest Stages page. Also, if you can drop it, it's not a Quest Item. And that it has monetary value will only further confirm this.
Granted, because he recommended it, it would probably make the quest go faster. But because you already finished the quest, I'm not sure how this would benefit anymore.