Image charge method to find Green's function

In summary, there are two general methods for determining the Green's function: using image charge and using orthonormal eigen functions. The main difference between these methods is that the image charge method may not always be applicable in practice. It is typically used for problems involving a point charge or a half-plane, but may also be used for two parallel plates by introducing an infinite series of image charges. Both methods will yield the same result when applicable.
  • #1
ahmad1992
5
0
hi guys,
my professor told me in the class that when we would like to determine green function there are two general method i.e using image charge and using orthonormal eigen function. However I don't understand what are the specific differences between them. Anybody can help me? Moreover in the problem systems that solved by using image charge (as far as I have seen), there is always point charge there. Can image charge method be used in a problem like finding green function in a space (without charge) between 2 infinite parallel conducting plates for example?
 
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  • #2
Can you give an example of finding Green's function by either method?
 
  • #3
That's why I am asking, can we use both of them for same problem or not ?
 
  • #4
ahmad1992 said:
Moreover in the problem systems that solved by using image charge (as far as I have seen), there is always point charge there. Can image charge method be used in a problem like finding green function in a space (without charge) between 2 infinite parallel conducting plates for example?
The Green's function is defined as the potential due to a point charge with all surfaces grounded.
The image charge method is difficult to use for 2 parallel plates, because that requires an infinite set of image charges.
 
  • #5
Oh unfortunately I have a task to solve it usi b g image charge
 
  • #6
The only difference between the two methods is that the image-charge method is not always applicable in practice. Of course, at the end you get the same result with both methods when applicable. It works for the half-plane and the sphere straight-forwardly. For two parallel plates I think you can use it, introducing an infinite series of image charges and summing up their contributions.

Since this is a typical home-work problem, you should ask this question in the homework section.
 

1. What is the Image Charge Method?

The Image Charge Method is a mathematical technique used to solve problems related to electric potential and charge distribution. It involves creating a mirrored or "image" charge in a different location to mimic the behavior of the original charge, making it easier to solve for the electric potential.

2. How does the Image Charge Method work?

The Image Charge Method works by using the principle of superposition, which states that the electric potential at any point is the sum of the contributions from all individual charges. By creating an image charge with opposite sign and placing it at a specific distance from the original charge, the resulting electric potential can be calculated using simple equations.

3. What is the significance of the Green's function in this method?

The Green's function is a fundamental concept in mathematics that is used to solve differential equations. In the context of the Image Charge Method, the Green's function represents the electric potential at a specific point due to a unit charge at a different point. It is a crucial component in solving for the electric potential using the Image Charge Method.

4. When is the Image Charge Method most useful?

The Image Charge Method is most useful for solving problems involving a single point charge and a conducting surface or boundary. It is also commonly used in problems where the distance between the original charge and the conducting surface is much smaller than the distance to the point of interest.

5. Are there any limitations to the Image Charge Method?

While the Image Charge Method is a useful tool in solving certain electrostatic problems, it does have its limitations. It is only applicable to problems involving a single point charge and a conducting surface, and it may not give accurate results for more complex charge distributions. Additionally, the method assumes that the conducting surface is perfectly conducting, which may not always be the case in real-world scenarios.

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