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§6.1–2 Magnetization
Christopher CrawfordPHY 311
2014-04-14
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HW 10 hints
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Outline• Multipoles – review compare: QE
– Internal, external• Magnetic Dipole m=I A compare: p=q d
– Dynamics – torque, potential, force compare: E– Diamagnetism compare: α– Paramagnetism compare: α
• Magnetization Density M=dm/dτ compare: P– Magnetization sheets – flow– Magnetization solenoids – flux compare: ΦP
– Magnetization currents Jb, Kb compare: ρb, σb
• Boundary value problem– Dipole sphere with surface current Kb compare: σb
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Multipoles – review• Electric multipoles
– No external monopole – just a constant potential offset
• Magnetic multipoles– Derivatives P’(x) –> there is NO monopole at all
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Magnetic dipole• Electric dipole
– Remember pure spherical surface charge dipole– Torque– Potential
• Magnetic dipole – Gilbert vs Ampere dipole– We will solve same BVP: spherical surface current dipole today– Torque– Potential
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Electric vs. magnetic dipole force• Electric dipole • Magnetic dipole
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Diamagnetism• Induced electric polarizability αe of all molecules
• Diamagnetism– Dipoles oriented opposite to field!– Compare direction of Eb, Bb
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Wikipedia: Magnetic_levitationA live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 Teslas
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Paramagnetism• Electric polarizability αe of permanent dipoles
• Paramagnetism– Exhibited in all atoms, stronger than diagmagnetism– often cancelled out by Pauli exclusion principle
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Magnetization density• Polarization density
– Polarization chains – flux– Bound charge
• Magnetization density– Magnetization mesh – flow– Magnetization solenoids – flux– Bound currents
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Calculation of bound potential
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Boundary value problem #1
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Boundary value problem #2
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