Conducting planes in magnetostatics

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Homework Help Overview

The problem involves two infinitely long perfectly conducting planes located at x = 0 and y = 0, creating a boundary in the upper right quadrant where a magnetic dipole is positioned. The task is to determine the magnetic field in this region using the method of images and considering the boundary conditions for magnetic fields.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster considers using the method of images and reflects on the significance of conducting plates in magnetostatics. Other participants question how boundary conditions would differ if the materials were dielectric instead of conducting.

Discussion Status

The discussion is ongoing, with participants exploring the implications of different material properties on boundary conditions. Some guidance has been provided regarding the trivial nature of dielectric boundary conditions, but no consensus has been reached on the broader implications.

Contextual Notes

Participants are navigating the complexities of boundary conditions in magnetostatics, particularly in relation to conducting versus dielectric materials. There is an indication that further resources, such as textbooks, may be beneficial for deeper understanding.

shehry1
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Homework Statement


Two infinitely long perfectly conducting planes at x = 0 and y = 0 form a boundary on the upper right quadrant (x > 0, y > 0). A magnetic dipole m = m_x + m_y [with their corresponding unit vectors] is located at at (x', y', z' = 0) in the upper right quadrant. Find the magnetic field everywhere in the upper right quadrant.

Now I think that I can solve the problem using method of images and the usual boundary conditions for normal B and tangential H. But what is the actual significance of conducting plates for magnetostatics?


Homework Equations





The Attempt at a Solution

 
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shehry1 said:
Now I think that I can solve the problem using method of images and the usual boundary conditions for normal B and tangential H. But what is the actual significance of conducting plates for magnetostatics?
You answered your own question in the previous sentence. :)
 
turin said:
You answered your own question in the previous sentence. :)

Well. To put it in another way. How would the boundary conditions change in case the sheets were made out of dielectrics. As far as I understand, there cannot be any difference.

Thanks a lot for answering. I had given up on it.
 
I will assume that you meant permeable material instead of dielectric. The dielectric boundary conditions on the magnetic field are trivial. What is the image of a magnetic dipole in a perfectly conducting surface? What is the image of a magnetic dipole in the surface of a permeable material? Do you have a textbook? The answers to these questions can be found in Jackson (with a little persistence).
 

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