W9_parallel_resonance.eps

Week 4: Capacitance 143

We still don’t knowallof Maxwell’s equations, but when we do, we will be forced to confrontthe
unpleasant truth that it is impossible for the electrons to be moving in“convenient” planetary-style
classical orbits and for Maxwell’s equations to be true. Of course wealso don’t know how to solve
the associated quantum problem. Se we might as well construct thesimplest possible model and
hope that it provides us with some insight.

Example 4.4.1: The Lorentz Model for an Atom

The model we will build is a to imagine the atom to consist of a pointlike nucleus surrounded by a
uniform ballof negative charge with a total charge of−Zeand a radiusa(whereais around one
angstrom). This is called theLorentz modelfor the atom, and works surprisingly well – so much
so that physics graduate students still use a dynamical version tounderstand dielectric polarization
and dispersion! See figure 44:

+Ze

−Ze

a

electron cloud

Figure 44: An “atom” consisting of a tiny massive nucleus surrounded by auniformball of negative
charge modelling the “electron cloud”.

Now we can easilycomputewhat will happen when we place this atom into a “weak” electric
field! We imagine that the field doesn’t change the shape or size of theelectron cloud but simply
diplaces the nucleus away from its equilibrium position in the center to anewequilibrium where
the force exerted on it by the external electric fieldE~ 0 balances the force on it due to the electron
cloud:

+Ze

−Ze

electron cloud

E

−ZeE

+ZeE 0

atom

Figure 45: An “atom” polarized by an external electric field.

The upward field isE 0 in the +zdirection. The electric field of a uniform distribution of−Ze