Final answer:
The magnetic field B inside the hollow interior (r < r1) of the cylindrical conductor with inner radius r1 and outer radius r2, which carries a current with current density J, is zero because no current is enclosed within this region as per Ampère's law.
Step-by-step explanation:
The student is dealing with a concept in physics, specifically within the study of electromagnetism. The scenario involves calculating the magnetic field inside the hollow region of a cylindrical conductor carrying a current. According to Ampère's law and using the symmetry of the problem, the magnetic field within a conductor depends on the distance r from the center and the current enclosed by an Ampèrian loop.
Since no current is enclosed within the hollow region (r < r1), the magnetic field B inside the hollow interior of the cylindrical conductor with inner radius r1 and outer radius r2 is zero. This can be deduced using Ampère's law, which relates the enclosed current to the magnetic field in a loop surrounding the current.
The physical phenomenon described here utilizes the principles of Ampère's law which is a fundamental equation in magnetostatics, a subfield of classical electromagnetism, indicating that the magnetic field in space can be calculated from the knowledge of the current distribution that produces it.