Conducting planes in magnetostatics

In summary, the problem involves two infinitely long perfectly conducting planes forming a boundary in the upper right quadrant, with a magnetic dipole located at a specific point in this quadrant. The solution can be found using the method of images and the usual boundary conditions for normal B and tangential H. The significance of conducting plates for magnetostatics is that they allow for a simple solution to this problem. If the plates were made out of permeable material, the boundary conditions would be different and the solution more complex. Additional information and guidance on this problem can be found in a textbook such as Jackson.
  • #1
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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  • #2
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. :)
 
  • #3
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.
 
  • #4
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).
 

Related to Conducting planes in magnetostatics

1. What are conducting planes in magnetostatics?

Conducting planes in magnetostatics are hypothetical surfaces that have perfect conductivity and are used to model the behavior of electromagnetic fields near highly conductive materials.

2. How do conducting planes affect magnetic fields?

Conducting planes can alter the behavior of magnetic fields by inducing eddy currents that oppose the original magnetic field, causing it to be weakened or redirected.

3. What is the significance of conducting planes in magnetostatics?

Conducting planes are important in understanding the behavior of electromagnetic fields near highly conductive materials, such as metals and alloys, which are commonly used in electrical devices.

4. How are conducting planes used in practical applications?

Conducting planes are used in the design and analysis of electromagnetic devices, such as transformers and motors, to predict and control the behavior of magnetic fields in the presence of conductive materials.

5. Are conducting planes limited to only magnetostatics?

No, conducting planes can also be used in other areas of electromagnetics, such as electrostatics and electrodynamics, to model the behavior of electric fields near conductive materials.

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