How Does Green's Function Simplify Understanding Electromagnetic Equations?

In summary, the conversation is about a person's struggle with understanding mathematical formulas and seeking help from others. They mention a specific relation and a polar form of a Laplace operator, but are having trouble understanding how to use it. They also mention a Green's function and ask for a simple explanation, providing links for further reading.
  • #1
AJ Bentley
668
0
I have a serious blind-spot with mathematics (but I keep trying)
Can someone help me with this.

I have a relation [tex]A = \mu_{0}/4\pi\int J/r \ dVol[/tex]

Which (apparently!) can be written [tex]\nabla^{2} A = - \mu_{0} J[/tex]

I know that [tex]\nabla^{2} A = 1/r \ \delta^{2} ( r A ) / \delta r^{2}[/tex]
which is the polar form of the Laplace operator

but I can't see how to use it to make the step.
The text refers to it as a Green's function but the explanations of that phrase look like a it would take me days to figure out what that means.
Is there a simple explanation?
 
Last edited:
Physics news on Phys.org

FAQ: How Does Green's Function Simplify Understanding Electromagnetic Equations?

What is a Green's function and why is it important in science?

A Green's function is a mathematical tool used to solve differential equations in physics and engineering. It represents the response of a system to a point source, and can be used to find the solution to a wide range of problems in various fields of science. Its importance lies in its ability to simplify complex problems and provide a general solution that can be applied to different scenarios.

How is a Green's function calculated and what is its mathematical representation?

A Green's function is typically calculated by solving the differential equation for a point source at the origin, and then applying boundary conditions to obtain a general solution. Its mathematical representation is a function that depends on the properties of the system being studied, and it is often expressed as an integral or a series of terms.

What are the properties of a Green's function and how are they used in scientific research?

A Green's function has several important properties, such as symmetry, positivity, and causality, which make it a powerful tool in scientific research. These properties can be used to analyze the behavior of a system, determine its stability, and predict its response to different stimuli.

In what fields of science is the concept of Green's function commonly applied?

The concept of Green's function is widely used in many fields of science, including physics, engineering, mathematics, and geology. It is particularly important in the study of electromagnetism, quantum mechanics, and fluid dynamics, but it can also be applied to other areas such as acoustics and heat transfer.

Are there any limitations to the use of Green's function in scientific research?

While Green's function is a useful tool in many scientific applications, it also has some limitations. For example, it may not always be possible to find an exact solution for a given problem, and in these cases, approximations or numerical methods may be needed. Additionally, Green's function may not be applicable to systems with highly nonlinear behavior or complex geometries.

Similar threads

A Square of an integral containing a Green's Function
Replies
7
Views
1K
A Green's function for Stokes equation
Replies
1
Views
2K
I Green's function boundary conditions
Replies
1
Views
704
A Green's function for problems involving linear isotropic media
Replies
3
Views
1K
I 4D d'Alembert Green's function for linearised metric
Replies
4
Views
2K
A How do we go from BVP to IVP in determining the Green's function?
Replies
1
Views
2K
I Linearised gravity approach to Lense Thirring metric
Replies
7
Views
971
I Understanding relationship between heat equation & Green's function
Replies
6
Views
2K
Finding electric potential using Green's function
Replies
7
Views
5K
Magnetic field of a rotating disk with a non-uniform volume charge
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top