Advanced E&M Phys 350

Chapter 4

The quiz will be available on Wednesday and should be completed by Friday before class.

Although Maxwell's equations provide the foundation of a fundamental theory they are almost useless on their own. The problem is that even though almost all physical phenomena that we observe can be traced back to electric and magnetic fields, the complexity of a first principles calculation in the presence of matter is impossible. In this chapter we will explore sound models for the behavior of macroscopic chunks of stuff in electric fields.

We began this discussion in chapter 2 when we developed a simplified model for conductors. We continue by describing a model for dielectrics.

Important ideas:

- dipole, remember that when we expanded the field in terms of moments each successive term dropped of faster with r. For our neutral dielectrics it is reasonable to imagine that considering it as an arrangement of dipoles might be a reasonable approximation if one doesn't look to closely.
- local dipoles (in dielectrics) are generated by the local field either by separating charge or by aligning already separated charge (atomic dipoles).
- dipole moment/ unit volume, P (vector quantity)
- equation 4.10 is a derived formulation of the potential in terms of P. Once you have checked the derivation notice that the 1
^{st}term is the same potential as that of a surface charge, while the second is the same as a charge density. Because we already know a good deal about the fields generated by charges it is easier to deal with the formulas in terms of these identifications. It is also possible to imagine how such charge densities might actually arise from the dipoles. - Identifying P as way to generate a bound charge and then using this bound charge to find the electric fields or potentials is the standard approach.
- To further aid in problem solutions the electric displacement D is introduced.

Summary

E remains the same as before we merely have to take into account the additional charges.

For the special case of linear dielectrics

where linear means

The definition of an energy associated with fields in the presence of dielectrics is complicated. For the case of linear dielectrics that do not have thermal losses.

This not the total energy of the system. Some of the energy associated with the assembly of the charges in the dielectric is ignored. This becomes the sensible definition of energy based on the types of problems one considers.

Things to be aware of:

- The fact that the curl of P and D result in new types of vector fields means that you cant apply intuition about E to P and D without care.

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