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## Magnetic Fields in Matter

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**Chapter 6**Magnetic Fields in Matter Department of Physics , ROCMA**Magnetization**Torques and Forces on Magnetic Dipoles rotation**Magnetization**paramagnetism random External B field Diamagnetism Ferromagnetism**Magnetization**Force on magnetic dipole Case of uniform field (B=constant): 0**Magnetization**Case of nonuniform field (B ≠ constant): y x Fringing field B I**Magnetization**z I y x**Magnetization**z I y x**Magnetization**+ Electric dipole - N Magnetic dipole I S Gilbert model Ampere model**Magnetization**Effect of magnetic field on atomic orbits**Magnetization**only electric force add magnetic field**Magnetization**when B is turn on,the electron speeds up.**Bound Currents**--Using Biot-Savart law**Bound Currents**Exp 1: Find the magnetic field at the center of a uniformly magnetized sphere.**Bound Currents**Exp 1:**Bound Currents**Exp 1: θ R**Bound Currents**Exp 1: b**Bound Currents**Find the magnetic field of point P.**Bound Currents**q2 q u q1 R**Physical Interpretation of Bound Currents**When the magnetization is uniform:**Physical Interpretation of Bound Currents**When the magnetization is nonuniform:**The Auxiliary Field H**Exp 2: A long copper rod of radius Rcarries a uniformly distributed (free) current I. Find H inside and outside the rod. • The Auxiliary Field H**The Auxiliary Field H**Exp 2:**A Deceptive Parallel**Ampere law in vacuum : Ampere law in magnetic materials : Whereas ,the divergence of is not, in general, zero.**Linear and Nonlinear Media**For linear isotropic homogeneous media Electric Magnetic**Linear and Nonlinear Media**Exp 3: An infinite solenoid (n turns per unit length, current I) is filled with linear material of susceptibility χ m. Find the magnetic field inside the solenoid.**Ferromagnetism**Ferromagnetic Materials : Fe, Co, Ni, Gd, Dy domain domain wall The domains range from about 10-12 to 10-8m3in volume and contain 1017 to 1021 atoms.**Ferromagnetism**Ferromagnetic domains. (photo courtesy of R. W. DeBlois)**Ferromagnetism**Hysteresis loop saturation remanence b c a g d f e coercive**Ferromagnetism**Hysteresis loop hard soft