If you put two square, neutral conductors in the middle of a uniform electric field such that they are touching, will they separate?
I thought yes. When they are touching, as shown in the picture, I consider them a single rectangular conductor and by Gauss's law there should be a net negative charge on one side and a net negative charge on the other side. Then each conductor would feel a net force and start moving. However, I don't know if something weird happens when they become separated that would make this less obvious than it seems.
Additionally, if they do separate, will they carry the net charges you calculate on each side using Gauss's law when they are together?