Do I need a new Visa if I change Universities?

At the moment I have a X1 which is valid for one year. I got it because i planed to study in Zhuhai for two semesters. Now I decided to go to Beijing for the second semester. The Beijing University already accepted my application.

Can i just use my original X1 for the second semester eventhough I change the city and the University? If I have to apply for a new one, can I do that from within mainland?
Thank you in advance!