1. 02/13/2015PHY 712 Spring 2015 -- Lecture 131 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 13: Continue reading Chapter 5 1.Hyperfine interaction 2.Macroscopic magnetization density M 3.H field and its relation to B 4.Magnetic boundary values

2. 02/13/2015PHY 712 Spring 2015 -- Lecture 132

3. Interactions between magnetic dipoles Sources of magnetic dipoles and other sources of magnetism in an atom: Intrinsic magnetic moment of a nucleus Intrinsic magnetic moment of an electron Magnetic field due to electron current Interaction energy between a magnetic dipole m and a magnetic field B: 02/13/2015PHY 712 Spring 2015 -- Lecture 133 r Hyperfine interaction energy:

4. 02/13/2015PHY 712 Spring 2015 -- Lecture 134 Hyperfine interaction energy: -- continued Evaluation of the magnetic field at the nucleus due to the electron current density: The vector potential associated with an electron in a bound state of an atom as described by a quantum mechanical wavefunction can be written: We want to evaluate the magnetic field in the vicinity of the nucleus

5. 02/13/2015PHY 712 Spring 2015 -- Lecture 135 Hyperfine interaction energy: -- continued

6. 02/13/2015PHY 712 Spring 2015 -- Lecture 136 Hyperfine interaction energy: -- continued Putting all of the terms together: In this expression the brackets indicate evaluating the expectation value relative to the electronic state.

7. 02/13/2015PHY 712 Spring 2015 -- Lecture 137 Macroscopic dipolar effects -- Magnetic dipole moment Note that the intrinsic spin of elementary particles is associated with a magnetic dipole moment, but we often do not have a detailed knowledge of J(r). Vector potential for magnetic dipole moment

8. 02/13/2015PHY 712 Spring 2015 -- Lecture 138 Macroscopic magnetization Vector potential due to “free” current J free (r) and macroscopic magnetization M(r). Note: the designation J free (r) implies that this current does not also contribute to the magnetization density.

9. 02/13/2015PHY 712 Spring 2015 -- Lecture 139 Vector potential contributions from macroscopic magnetization -- continued

10. 02/13/2015PHY 712 Spring 2015 -- Lecture 1310 Vector potential contributions from macroscopic magnetization -- continued

11. 02/13/2015PHY 712 Spring 2015 -- Lecture 1311 Magnetic field contributions

12. 02/13/2015PHY 712 Spring 2015 -- Lecture 1312 1 2

13. 02/13/2015PHY 712 Spring 2015 -- Lecture 1313 1 2

14. 02/13/2015PHY 712 Spring 2015 -- Lecture 1314 Example magnetostatic boundary value problem M0M0

15. 02/13/2015PHY 712 Spring 2015 -- Lecture 1315 Example magnetostatic boundary value problem -- continued M0M0

16. 02/13/2015PHY 712 Spring 2015 -- Lecture 1316 M0M0 Example magnetostatic boundary value problem -- continued

17. 02/13/2015PHY 712 Spring 2015 -- Lecture 1317 M0M0 Example magnetostatic boundary value problem -- continued

18. 02/13/2015PHY 712 Spring 2015 -- Lecture 1318 Check boundary values:

19. 02/13/2015PHY 712 Spring 2015 -- Lecture 1319 Variation; magnetic sphere plus external field B 0 M0M0 B0B0

20. 02/13/2015PHY 712 Spring 2015 -- Lecture 1320 1 2

21. 02/13/2015PHY 712 Spring 2015 -- Lecture 1321 Magnetism in materials

22. 02/13/2015PHY 712 Spring 2015 -- Lecture 1322 Example: permalloy, mumetal  0 ~ 10 4    a b B0B0 Spherical shell a < r < b :

23. 02/13/2015PHY 712 Spring 2015 -- Lecture 1323 Example: permalloy, mumetal  0 ~ 10 4 -- continued    a b B0B0

24. 02/13/2015PHY 712 Spring 2015 -- Lecture 1324 Example: permalloy, mumetal  0 ~ 10 4 -- continued    a b B0B0

25. 02/13/2015PHY 712 Spring 2015 -- Lecture 1325 Example: permalloy, mumetal  0 ~ 10 4 -- continued    a b B0B0

26. 02/13/2015PHY 712 Spring 2015 -- Lecture 1326 Example: permalloy, mumetal  0 ~ 10 4 -- continued    a b B0B0

27. 02/13/2015PHY 712 Spring 2015 -- Lecture 1327 Energy associated with magnetic fields