Abstract: Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and responses to conceptual questions, we document specific resources employed by students when reasoning about the divergence of a vector field. One common student error, which persisted in our course despite explicit instruction, is to misinterpret any "spreading out" of field lines in a diagram as representing a place of non-zero divergence. Some of these student difficulties can likely be attributed to having first learned about the divergence in a mathematical context, where there was little emphasis on graphical representations and physical applications.
Keywords: physics education research, electromagnetism, divergence, mathematics, conceptual understanding.
PACS: 01.40.Fk, 01.50.Kw.