Final answer:
The rapid change of an electric field induces a magnetic field, as per Maxwell's equations and specifically Faraday's law of induction, which is a fundamental concept in the generation and propagation of electromagnetic waves.
Step-by-step explanation:
The rapid change of an electric field induces a magnetic field. This is a fundamental principle of electromagnetism encapsulated by Maxwell's equations. Specifically, Faraday's law of induction states that a changing magnetic flux induces an electric field, and Maxwell added that a changing electric field also generates a magnetic field. This relationship is at the core of how electromagnetic waves are formed, where a changing electric field gives rise to a magnetic field and vice versa, allowing the wave to propagate through space.
An example of this phenomenon is turning on a light switch, which initiates a change in the electric field that in turn generates a magnetic field. This magnetic field can induce an emf (electromotive force) in nearby conductive materials, according to Faraday's law. Hence, the correct answer to the student's question is 'B) a magnetic field.'