In far-field electromagnetic wave propagation, the electric field (E) and the magnetic field (B) are in phase with each other. This behavior arises due to the fundamental relationship between the two fields, known as Maxwell's equations.
Maxwell's equations describe the behavior of electromagnetic waves and how they propagate through space. One of these equations, known as Faraday's law of electromagnetic induction, states that a changing magnetic field induces an electric field. Similarly, another equation, Ampere's law with Maxwell's addition, states that a changing electric field induces a magnetic field.
When an electromagnetic wave propagates through space, it consists of mutually perpendicular electric and magnetic fields that oscillate in time. As the wave moves forward, the electric field oscillates in one direction, and this changing electric field induces a magnetic field according to Faraday's law. The induced magnetic field then propagates alongside the electric field.
Since the magnetic field is induced by the changing electric field, it lags behind the electric field by a quarter of a wavelength in space. However, as the wave propagates, both fields continue to oscillate and evolve together. As a result, the electric and magnetic fields remain in phase with each other at any given point in space during far-field propagation.
This phase relationship between the electric and magnetic fields is an inherent characteristic of electromagnetic waves and is crucial for the wave's energy transport and electromagnetic interactions.