Electromagnetic Help: Finding Suitable Green Function

Thread starter montser
Start date Apr 14, 2006
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Electromagnetic

In summary, the green function is a mathematical tool that is used to solve partial differential equations in electromagnetic problems. It helps to describe the relationship between a source and its effect on the surrounding space and can be used to find solutions for a wide range of boundary conditions. When selecting a green function for an electromagnetic problem, factors such as the type of source, boundary conditions, and geometry should be considered. The use of a green function simplifies the solution process by expressing it in terms of a single integral. While the green function approach can be applied to a wide range of problems, its accuracy depends on the appropriate selection and implementation. An incorrect or inadequate choice of green function can lead to errors in the solution, making it essential to carefully consider its

Apr 14, 2006

montser

electromagnetic help!

I have a general question on finding the suitable green function for a given potential for example:
Find the suitable green function for [itex]\nabla^2 \varphi= \frac{1}{l^2} \exp (\frac{-|x|}{l})[/itex]

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Apr 14, 2006

Meir Achuz

Science Advisor

Homework Helper

Gold Member

I didn't get to see your Qus.pdf, but if the only BC is \phi-->0 as
r-->infinity, then G=-1/{4\pi|r-r'|}.

FAQ: Electromagnetic Help: Finding Suitable Green Function

What is the purpose of finding a suitable green function in electromagnetic problems?

The green function is a mathematical tool used to solve partial differential equations in physics, including electromagnetic problems. It helps to describe the relationship between a source and its effect on the surrounding space, and can be used to find solutions for a wide range of boundary conditions.

What factors should be considered when selecting a green function for an electromagnetic problem?

There are several factors to consider when choosing a suitable green function, including the type of source, the boundary conditions, and the geometry of the problem. It is also important to ensure that the green function satisfies the necessary mathematical properties, such as being continuous and differentiable.

How does the use of a green function simplify the solution of an electromagnetic problem?

The green function allows for the solution of an electromagnetic problem to be expressed in terms of a single integral, rather than a more complex combination of integrals and derivatives. This simplifies the calculation process and makes it easier to obtain a solution for the problem.

Can the green function be used to solve any type of electromagnetic problem?

The green function approach is a powerful mathematical technique that can be applied to a wide range of electromagnetic problems. However, it may not be suitable for more complex problems that involve nonlinear or time-dependent phenomena.

How does the choice of a green function affect the accuracy of the solution for an electromagnetic problem?

The accuracy of the solution depends on the appropriate selection and implementation of the green function. If the chosen green function does not accurately represent the problem or is not applied correctly, it can lead to errors in the solution. Therefore, it is important to carefully consider the choice of green function to ensure an accurate solution.