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Electromagnetic Wave Equation

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...

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The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...

Plane Electromagnetic Waves II

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Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between electric and magnetic fields with the help of Faraday's law.

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Magnetic Vector Potential

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...

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Related Experiment Video

Updated: Jun 26, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

The van Cittert-Zernike theorem for electromagnetic fields.

Andrey S Ostrovsky¹, Gabriel Martínez-Niconoff, Patricia Martínez-Vara

¹Universidad Autónoma de Puebla, Facultad de Ciencias Físico Matemáticas, Puebla 72000, Mexico. andreyo@fcfm.buap.mx

|February 4, 2009

Summary

This summary is machine-generated.

The van Cittert-Zernike theorem is now generalized for vector electromagnetic fields. This new theorem reveals that coherence increases during propagation, while polarization remains constant for incoherent vector sources.

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Area of Science:

Optics and Photonics
Electromagnetism
Classical Field Theory

Background:

The van Cittert-Zernike theorem is a fundamental concept in scalar optical field theory.
Generalizing this theorem to vector fields is crucial for understanding complex electromagnetic phenomena.

Purpose of the Study:

To generalize the van Cittert-Zernike theorem for vector electromagnetic fields.
To analyze the behavior of coherence and polarization during propagation from incoherent vector sources.

Main Methods:

Mathematical derivation and generalization of the van Cittert-Zernike theorem for vector fields.
Optical simulation of secondary sources with controlled statistical properties.

Main Results:

The generalized theorem demonstrates that the degree of coherence of electromagnetic fields from incoherent vector sources increases upon propagation.
The degree of polarization of these fields remains invariant during propagation.
Demonstrated application through optical simulation of partially coherent and polarized secondary sources.

Conclusions:

The generalization provides new insights into the propagation characteristics of vector electromagnetic fields.
The findings have potential applications in controlling and manipulating the statistical properties of light sources.