What background question should I choose for my study?
The topic of the research is "split of university campuses and its effect on students."
Your question is slightly unclear. I think you are confusing between the background of the study and research question. The background of a study establishes the context of the research. This section explains why the research topic you have chosen is important. A well-written background is essential to understanding the main aspects of the study. Usually, the background forms the first section of a research article/thesis and justifies the need for conducting the study and summarizes what the study aims to achieve.
The research question is a concisely written question that investigates a topic being studied (purpose), the variable(s), and the population. Choosing the right research question is the first and most important step toward publication.
Since you have already identified a topic, it is best that you do an exhaustive literature review to know what has already been investigated on that particular topic. You may also take help of some specific frameworks developed to help researchers formulate research questions step by step and factor by factor. You should avoid research questions that are too easy as well as ones that are interesting but not practically possible to work on. An ideal research question is one that combines feasibility with interest.