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If a current is above a conducting surface, why do we take the image of the current to find the magnetic field intensity? Why not just take the effect of the actual current only? And are this method and equations applied to satisfy boundary conditions at the surface?

Also, is there any good tutorial that explains the method of images in magnetostatics because I could not find any?

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  • $\begingroup$ In slide 22 of this presentation(ocw.mit.edu/courses/electrical-engineering-and-computer-science/…) you can find a good tutorial. The method of image is used to ensure boundary conditions are met at boundary surface $\endgroup$
    – Gotaquestion
    Commented Nov 17, 2013 at 21:32
  • $\begingroup$ ok but i got thus case but still not understanding the case when current in a medium with mu1 and the boundary surface is another medium mu2 the methods of image here is not clear why when calculating field in second medium we tale effect of current in medium 1 that is related in its value to actual current and mu1,mu2 why here there is no image current $\endgroup$
    – Mai Fouad
    Commented Nov 18, 2013 at 7:19
  • $\begingroup$ The method of image is used when one of the mediums is a perfect electric conductor. The method is a trick to unsure that the boundary conditions at the interface between the two mediums is properly satisfied. In electrostatic case, if one of the mediums is a perfect electric conductor it doesn't make a difference what its epsilon is because conductivity overrides permitivity sort of say. I would assume the same is true for magnetostatics,you only use image method to study perfect conductor case which makes mu2 irrelevant @MaiFouad $\endgroup$
    – Gotaquestion
    Commented Nov 18, 2013 at 10:06
  • $\begingroup$ but see the case that i mentioned in this reference page 280-282 books.google.com.eg/… $\endgroup$
    – Mai Fouad
    Commented Nov 18, 2013 at 15:00
  • $\begingroup$ I see, but you are asking about a conducting surface, so the dielectric case is different from what you are asking about, right? @MaiFouad $\endgroup$
    – Gotaquestion
    Commented Nov 18, 2013 at 15:48

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The current creates a magnetic field. The magnetic field has to satisfy the appropriate boundary conditions at the interface between the medium in which the current is flowing and the perfect conductor.

The method of image is a mathematical tool applied to ensure that the magnetic field at the interface between the two mediums satisfies the boundary conditions. It was originally developed to solve for electrostatic charges, then it was extended to magnetostatics and time varying magnetic fields. Have a look at chapter 4 of Pramanik book. Also, have a look at this paper for a review of method of image for electrostatic, magnetostatic and electromagnetic cases.

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  • $\begingroup$ What's pramanik book @gotaquestion? $\endgroup$
    – Apoorva Shukla
    Commented Jul 25 at 15:55

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