Understanding the Phase Relationship Between Electric and Magnetic Fields in Electromagnetic Waves

The phase relationship between the electric and magnetic fields in an electromagnetic wave is a fundamental concept in the study of electromagnetic theory. This article aims to clarify the current understanding and historical perspectives on this topic, emphasizing the co-relationship between the phases of the electric and magnetic fields and the implications for our comprehension of electromagnetic wave behavior.

Maxwell's Equations and Phase Relationship

According to Maxwell's equations, the electric field E and the magnetic field B are always in phase in radiated electromagnetic fields. This means that they oscillate in synchrony and share the same phase, leading to a phase difference of 0 degrees or 0 radians.

The mathematical representation of the electric field Et and the magnetic field Bt can be expressed as:

Et E0sin(kx - ωt)

Bt B0sin(kx - ωt)

Here, E0 and B0 represent the amplitudes, k is the wave number, and ω is the angular frequency. Since both functions have the same argument, they oscillate in sync, confirming that their phase difference is indeed 0.

Intuitive Understanding and Experimental Evidence

However, many people argue that, based on our intuitive understanding, there should be a 90-degree phase difference between the electric and magnetic fields. This phase difference would enable the change in electric field to cause the magnetic field, and vice versa, allowing the energy to be continuously converted between the two fields.

According to the textbook on radiated electromagnetic fields, there is no 90-degree phase difference. This is the result calculated according to Maxwell's equations. Nonetheless, Hertz's experiments showed that the phase difference can indeed be 90 degrees under certain conditions.

In the context of near fields, the phase difference of 90 degrees exists, and it is possible that this might be the case for far fields as well. This is because classical electromagnetic theory typically ignores the effects of advanced waves. Advanced waves, which also satisfy Maxwell's equations, are not considered in classical theory, which explains the 90-degree phase difference in the near field.

New Developments and Theories

Recent developments in electromagnetic field theory, such as the mutual energy flow theory proposed by Zhao Shuangren, provide a more comprehensive explanation of the phase relationship between the electric and magnetic fields.

Zhao Shuangren's mutual energy flow theory extends the electromagnetic mutual energy theorem, which is equivalent to a law of energy conservation for electromagnetic fields. This theory introduces the concept of advanced and retarded waves, which together form the mutual energy flow. The mutual energy flow can be considered as the photon, while the electromagnetic wave is composed of the retarded wave from the light source and the advanced wave from the light sink.

This theory not only acknowledges the 90-degree phase difference but also explains the self-energy flow radiation as a reactive power wave. This means that the energy radiation is transmitted by mutual energy flow, replacing the conventional understanding of energy loss in electromagnetic waves.

Conclusion

In summary, the phase relationship between the electric and magnetic fields in an electromagnetic wave is a complex topic with implications for both theoretical physics and practical applications. While classical electromagnetic theory posits that the fields are in phase, advanced theories such as the mutual energy flow provide a more nuanced understanding that may offer new insights into the behavior of electromagnetic waves.

Keywords: electromagnetic wave, phase difference, electric field, magnetic field