Image charge method to find Green's function

[ahmad1992]

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?

 

[HallsofIvy]

Can you give an example of finding Green's function by either method?

 

[ahmad1992]

That's why I am asking, can we use both of them for same problem or not ?

 

[Meir Achuz]

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.

 

[elsafo]

Oh unfortunately I have a task to solve it usi b g image charge

 

[vanhees71]

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.