We investigate learning difficulties among second-year students in electromagnetism courses when they apply Amp`ere-Maxwell’s law. Using phenomenography, we analyzed written answers from 65 undergraduate physics students to four questions on Amp`ere’s and Amp`ere-Maxwell’s laws. We complemented our research by interviewing 12 students. To design the questionnaire, we ran an epistemological analysis of classical electromagnetism which helped us to identify a set of key essential concepts to understand this theory, guided the definition of learning objectives, and drew up the questions. The results revealed that the students found it hard to recognize the validity framework from Amp`ere’s law and to apply Amp`ereMaxwell’s law. They face particular difficulties to recognize the appearance of the displacement current and the relationship between the circulation of the magnetic field and an electric field that is variable over time.