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Fields and Waves Lesson 4.6 MAGNETIC MATERIALS Darryl Michael/GE CRD
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Magnetic Materials Today’s Lesson: linkage between H and B fields
M - magnetization re-visit Ampere’s Law boundary conditions permanent magnets
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Magnetic Materials Vast majority of materials Magnetic properties tend to either very strong or very weak ferromagnets (Fe) and permanent magnets Use simple, linear model exhibit strong non-linear effects demonstrate “memory” or hysterisis effects Recall in electrostatics that most materials have moderate effect: 1 < e < 10
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Magnetic Materials In Quantum mechanics, atoms have “spin”
In the classical picture: electron orbits the nucleus acts like a current loop Usually in most materials, the loops has random orientation - so the net effect is small In ferromagnets, neighboring atoms have spins that are aligned - strong effects
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Magnetic Dipole Moment
The individual current loops can be thought of as having a dipole moment,
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Relationship between & In general, one can write: magnetization
Sum over all atoms -flux due to all sources where, -flux due to atomic sources -flux due to free current (e.g. conduction current, e-beam)
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Relationship between & Maxwell’s equation:
these are free-currents Maxwell’s equation: we can determine H without determining M In most general form: If, Values, most materials for iron
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Curves for & Typical B-H Curve for materials
For course, use ideal curve: H B
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Boundary Conditions Do problem 1a: use then apply Boundary Conditions:
Normal component: h a Material 1 Material 2 TOP BOTTOM Take h << a (a thin disc) ignore contribution from the sides
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Boundary Conditions Boundary Conditions: Tangential component:
h << w Material 1 Material 2 w h Inet can only be due to surface currents = Js.w Surface currents - out of plane or If non-conductor, Js = 0 ,then, If conductor in 1 and
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Magnetic Materials Do Problems 1b and 2
Problem 2 : Field lines exit normally in high m materials Also, field lines like to travel through high m materials Transformers : use IRON to direct flux primary and secondary windings intercept almost all the flux - no need for “smoothly-wound” coils Noise reduction increase Inductance with increasing m Do Problem 3
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Magnetic and Electric Dipole Moment
The current loop approximates the dipole moment, E-field of electric dipole B-field of magnetic dipole Far-fields look the same for both types of dipoles
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