§6.1–2 Magnetization

Christopher CrawfordPHY 311

2014-04-14

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

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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