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325_Sp2010_10_Magnetic_materials_and_BC - 11 Brief overview...

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11. Brief overview of magnetic materials and boundary and boundary conditions for H and B fields EE325 Mikhail Belkin, EE 325, ECE Dept., UT Austin 1 Mikhail Belkin R 0 A= R 0 2 | m |=I A Summary of the previous lecture material Magnetic dipole and its magnetic field – At r>> R 0 , a loop of current behaves as a magnetic dipole – Magnetic dipole moment: mI A n ˆ – Magnetic field: Poisson’s’ and ‘Laplace’s’ equations for magnetic vector potential , , 0 3 3 4 mrr m B r ˆˆ H J   B A  0 BH 0 A J  Mikhail Belkin, EE 325, ECE Dept., UT Austin 2 and we know that we can use A with – The equation for A : where  2 A AA    0 A   2 0 A J  22 2 2 x yz A xA yAzA    ˆ
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Magnetic materials A volume of material contain many atomic magnetic moments. In the absence of external magnetic field they are typically randomly oriented like this. Once external magnetic field is applied the individual magnetic dipole experience torque that aligns them like that shown below. As a result, we have magnetization: Some atoms or molecules (e.g., water) don’t have magnetic moment. In this case the magnetic moment may be induced and is Mikhail Belkin, EE 325, ECE Dept., UT Austin 3 may be induced and is typically in the direction opposite to applied field (not shown here). These materials are diamagnetic. The effect is usually very small and these materials may be considered nonmagnetic for many practical purposes. Magnetic materials in a manner very similar to dielectrics, magnetic dipole moments can align and enhance or reduce applied magnetic field these materials are not as common as “dielectrics” Magnetization (compare with polarization in dielectrics) is given as: MNm  m ext M H and
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325_Sp2010_10_Magnetic_materials_and_BC - 11 Brief overview...

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