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Physical interpretation of bound currents

Physical interpretation of bound currents. volume bound current surface bound current. Net effect: macroscopic current flowing over the surface of magnetized object.

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Physical interpretation of bound currents

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  1. Physical interpretation of bound currents volume bound current surface bound current Net effect: macroscopic current flowing over the surface of magnetized object Left: A schematic view of how an assembly of microscopic dipoles appears like a macroscopically separated pair of charged sheets, as shown at top and bottom (these sheets are not intended to be viewed as originating the electric field that causes the dipole alignment, but as a representation equivalent to the dipole array); Right: How an assembly of microscopic current loops appears as a macroscopically circulating current loop. Inside the boundaries, the individual contributions tend to cancel, but at the boundaries no cancellation occurs. If the magnetization is nonuniform, the internal currents no longer cancel!

  2. Magnetic field inside matter Remember: in macroscopic picture of magnetic materials, one assumes spatial averaging over regions large enough to contain many atoms. It is useful to separate the charge density into the bound current Jb and free current Jf: Ampere’s law Total free current passing through the Amperian loop

  3. Example: A long copper rod of radius R carries a uniformly distributed free current I. Find H inside and outside the rod. For r<R: For r>R: Since outside the rod M=0, How to determine B inside the rod?

  4. Magnetostatic boundary conditions

  5. Magnetic Susceptibility and Permeability The volume magnetic susceptibility cm is defined by the relationship: If cm is positive the material is called paramagnetic, and the magnetic field is strengthened by the presence of the material. If is negative then the material is diamagnetic and the magnetic field is weakened in the presence of the material. The magnetic susceptibilities of paramagnetic and diamagnetic materials are generally extremely small. The magnetic susceptibility of most crystals is not a scalar. Magnetic response M is dependent upon the orientation of the sample and can occur in directions other than that of the applied field H. In these cases, volume susceptibility is defined as a tensor

  6. For linear media permeability Show how B and H are refracted at the boundary for the simple case where B and H are collinear in each medium and the free surface current density vanishes. 1 2

  7. How to measure B and H in solids?

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