What happens to a bag of holding in an Antimagic Field?

During a difficult fight, the wizard of the party decided to launch an antimagic field. It proved to be quite useful and let the warriors almost take out the opposing wizard. Nevertheless, multiple questions arose during the fight concerning what was happening in the field. One of them is about the heroes that have a bag of holding.

What would happen to these? Should they burst because of what’s inside? Should they return to normal, and the stuff in them be lost into oblivion? Nothing? Do you see any other problems that would happen with magical objects going into the field? (I’m afraid to miss something.)