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§6.1–2 Magnetization

§6.1–2 Magnetization. Christopher Crawford PHY 311 2014-04-14. HW 10 hints. Outline. Multipoles – review compare: Q E Internal, external Magnetic Dipole m =I A compare: p =q d Dynamics – torque, potential, force compare: E Diamagnetism compare: α

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§6.1–2 Magnetization

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  1. §6.1–2 Magnetization Christopher Crawford PHY 311 2014-04-14

  2. HW 10 hints

  3. Outline • Multipoles– reviewcompare: QE • Internal, external • Magnetic Dipole m=IAcompare: p=qd • Dynamics – torque, potential, forcecompare: E • Diamagnetism compare: α • Paramagnetism compare: α • Magnetization Density M=dm/dτcompare: P • Magnetization sheets – flow • Magnetization solenoids – fluxcompare: ΦP • Magnetization currents Jb, Kbcompare: ρb, σb • Boundary value problem • Dipole sphere with surface current Kbcompare: σb

  4. Multipoles – review • Electric multipoles • No external monopole – just a constant potential offset • Magnetic multipoles • Derivatives P’(x) –> there is NO monopole at all

  5. 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

  6. Electric vs. magnetic dipole force • Electric dipole • Magnetic dipole

  7. Diamagnetism • Induced electric polarizability αe of all molecules • Diamagnetism • Dipoles oriented opposite to field! • Compare direction of Eb, Bb Wikipedia: Magnetic_levitation A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 Teslas

  8. Paramagnetism • Electric polarizability αe of permanent dipoles • Paramagnetism • Exhibited in all atoms, stronger than diagmagnetism • often cancelled out by Pauli exclusion principle

  9. Magnetization density • Polarization density • Polarization chains – flux • Bound charge • Magnetization density • Magnetization mesh – flow • Magnetization solenoids – flux • Bound currents

  10. Calculation of bound potential

  11. Boundary value problem #1

  12. Boundary value problem #2

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