Advanced E&M Phys 350

Chapter 6

We need to have a comfort level with the way dipoles can be aligned with external fields. For dielectrics we discussed the possibility if separating charge in a material to create a dipole in response to an applied field. We also saw that some atoms and molecules already have natural dipole moments and these moments can line up in the presents of an external field.

 

For magnetic materials we have spin magnetic dipoles. Electrons and proton have natural magnetic moments due to spin. Just as in the case of electric materials these dipoles will tend to line up with the applied field.

 

Lining up electron dipole moments:

Remember the field at the center of the dipole is directed oppositely for charge and current dipoles.

Orbiting electrons also have magnetic moments (current loops) and an external field will change the orbits. This type of change tends to reduce aligned magnetic moments and increase anti aligned. The effect is an overall moment anti aligned with the field.

 

Impact on current loops:

 

 

Quantum spin spin interaction cause the electron magnetic moments to naturally line up in regions of the material (domains).

 

Spin-spin interaction in special materials:

 

So magnetic materials are more complicated in their response but the response is still simply characterized by a dipole moment/unit volume M.

For a general M(r) for some material we can view this as a bound current density inside the material Jb and a current density Kb on the surface.

We introduce an H field similar to the D field in dielectrics.

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