Using Green's functions in electrostatics

In summary, I'm having a hard time understanding Green's functions and I'm looking for a more intuitive physics reference.
  • #1
quasar_4
290
0
Hi everyone.

I'm in my first semester of Jackson right now, and most of it's fine, but I'm having a hard time understanding the use of Green's functions as Jackson describes them in chapters 1-4. Does anyone know of another good physics reference that might be more clear? I have plenty of the math methods type books, but I'm specifically looking for more connection to physics and building the Green's function approach into my physics intuition.

If this post is too vague, I can pinpoint a couple of specific problems that have given me headaches.

Thanks,

quasar_4
 
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  • #2
quasar_4 said:
Hi everyone.

I'm in my first semester of Jackson right now, and most of it's fine, but I'm having a hard time understanding the use of Green's functions as Jackson describes them in chapters 1-4. Does anyone know of another good physics reference that might be more clear? I have plenty of the math methods type books, but I'm specifically looking for more connection to physics and building the Green's function approach into my physics intuition.

If this post is too vague, I can pinpoint a couple of specific problems that have given me headaches.

Thanks,

quasar_4

I've looked at a number of physics books that cover this and they all seem unintuitive to me. I'll offer (a possibly controversial) suggestion. You could try electrical engineering texts on system theory. Here the Green's function approach (at least a special case of it) is used extensively. The strange thing is that you rarely see the term "Green's Function" in these texts. Instead system impulse response is considered, but the formalism is the same.

I'm an electrical engineer that took many physics courses. As an undergrad, I remember studying the Green's function approach in a "Mathematical Methods of Physics" class. I was confused at first and then realized linear system theory used this extensively. Somehow, system theory is an easier context to make sense of the principles. I sometimes wonder if electrical engineers long ago banished the term "Green's function" for being too intimidating. :smile: (well you do see it at the grad level, but there you can't hide from the mathematicians and physicists)

The following text is a good book on the subject, but it's not the only one. In this book, chapters 1 and 2 would be enough to show just how intuitive, simple and powerful the Green's function method is. I don't recommend buying a brand new hard cover book for this purpose, but if you can find it used or in soft-cover, or better yet at the library, I would recommend it. The first edition might even be better for your purpose.

https://www.amazon.com/dp/0138147574/?tag=pfamazon01-20
 
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  • #3
Chapter 5 of Franklin's "Classical Electromagnetism" cover Green's functions in electrostatics from a physical viewpoint.
 
  • #4
I agree with Steven.
Engineering text sometimes teaching better physics than physics textbook.
I do not understand why anybody wants to read Jackson. It is more like a reference than a textbook. There are so many pedagocially better books than Jackson or another one (Goldstein, yaks).
 
  • #5


Hi quasar_4,

Green's functions are a very useful tool in electrostatics as they allow us to solve complex problems by breaking them down into simpler parts. Essentially, Green's functions are mathematical functions that can be used to solve differential equations in a specific domain. In electrostatics, they are often used to solve for the electric potential or field in a given region, given a known charge distribution.

I understand that Jackson's explanation of Green's functions may be difficult to understand, as it can be quite mathematical. However, there are other resources available that may provide a clearer understanding of their use in electrostatics. One suggestion is the book "Classical Electrodynamics" by John David Jackson, which provides a more physics-focused approach to understanding Green's functions.

Additionally, you can try looking for online resources or lectures that specifically discuss Green's functions in electrostatics. These may provide a more intuitive explanation and help build your understanding of their use in physics.

If you have specific problems that have given you headaches, I would be happy to help you work through them and provide a clearer explanation. Just let me know and I will do my best to assist you.

I hope this helps and good luck with your studies!
 

1. What is a Green's function in electrostatics?

A Green's function in electrostatics is a mathematical tool used to solve problems in electrostatics. It represents the response of a system to a point source of electric charge at any given point in space.

2. How is a Green's function used in electrostatics?

A Green's function can be used to determine the electric potential at any point in space due to a given charge distribution. By convolving the Green's function with the charge distribution, the potential can be calculated at any point.

3. What are the advantages of using Green's functions in electrostatics?

Green's functions allow for a more efficient and elegant solution to electrostatic problems compared to other methods. They also provide a general solution that can be applied to a variety of different boundary conditions.

4. Are there any limitations to using Green's functions in electrostatics?

One limitation is that Green's functions are only applicable to linear systems. They also require the use of complex mathematical techniques, making them less accessible to those without a strong mathematical background.

5. Can Green's functions be used in other areas of physics?

Yes, Green's functions have applications in various areas of physics such as electromagnetism, quantum mechanics, and fluid dynamics. They are a powerful tool for solving differential equations and can be adapted to different physical systems.

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