The method of images can also be applied to certain magnetostatic problems. Consider a str...

The method of images can also be applied to certain magnetostatic problems. Consider a straight, thin conductor in air parallel to and at a distance d above the plane interface of a magnetic material of relative permeability µr. A current I flows in the conductor.

a) Show that all boundary conditions are satisfied if

i) the magnetic field in the air is calculated from I and an image current Ii,

and these currents are equidistant from the interface and situated in air;

ii) the magnetic field below the boundary plane is calculated from I and - I;, both at the same location. These currents are situated in an infinite magnetic material of relative permeability µr.

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b) For a long conductor carrying a current l and for µr » 1, determine the magnetic flux density B at the point P in Figure.

Figure: A current-carrying conductor near a ferromagnetic medium