Consider the case of a grounded conducting plane in the presence of a dipole p at a distance d. Find the image dipole p’ that allows this problem to be treated as a combination of just two dipoles, the real and the image. I need to know how to derive p'

Question

farcher · Answer

Image dipole is as far behind the conducting plane  as the dipole is in front and the line joining them is perpendicular to the  conducting plane.
The sign of any charge is switched.  Positive in the dipole becomes negative in the image dipole .

anonymous · Answer

Yes I know that part but I need to know how to prove p' without assuming that. Just need to find what p'= compared to p. So mathematically I have to show p' is same in magnitude but opposite for the x and y coordinates.

masumanwar · Answer

dipole moment P =qd

farcher · Answer

I now understand you question. The proof as to the validity of the use of image charges is well documented on the Internet. You will be able to find numerous references by Googling "Method of image charges". Here is one that does it fairly comprehensively with a good explanation. http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter3/LectureNotesChapter3.html