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quantum123
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How does Green's function work in electromagnetism?
quantum123 said:How do you prove the Jefimenko's Equations ? In some textbooks , these are proved from the retarded potentials, which are in turn proved by Green's functions, but how do you prove the existence of Green's functions and that they work?
kcdodd said:The simplest way to think of greens functions I have seen is as an inverse operator. For instance, creating an inverse to the laplace operator in electrostatics will give back the full potential.
quantum123 said:Wow, it is that simple?
I have found something here, that seems to agree with what you said:-
http://www.hep.upenn.edu/~rreece/docs/notes/jefimenko_equations.pdf
The Green's function in electromagnetism is a mathematical tool used to solve differential equations that describe the behavior of electric and magnetic fields. It represents the response of a system to a point source located at a specific point in space and time.
The Green's function is used to solve boundary value problems in electromagnetism, where the electric and magnetic fields are known at the boundaries of a region and the goal is to find the fields inside that region. It is also used to calculate the electric and magnetic fields generated by a distribution of charges or currents.
The Green's function in electromagnetism has several important properties, including linearity, symmetry, and causality. It is also a solution to the homogeneous wave equation and satisfies certain boundary conditions.
The Green's function in electromagnetism is calculated using the method of images, where the point source is replaced by a set of point sources located at the appropriate positions. It can also be calculated using integral transforms or numerical methods.
The Green's function in electromagnetism has many applications in physics and engineering, such as in antenna design, signal processing, and electromagnetic compatibility. It is also used in the study of electromagnetic radiation and scattering from objects, as well as in the development of electromagnetic simulation software.