Why can't I get inside the College of Winterhold? [duplicate]
Solution 1:
When you first talked to Faralda, did you give her a magic demonstration? She should have asked you to cast a spell either on her, or onto the symbol at her feet. Once you have done so, the locked door will be gone and you will be free to enter the college. If you do not have the spell she's looking for, she will teach it to you for a cheap price of 30 gold.
It is also possible to by pass her if your speechcraft is high enough.