Electric Charges and their Properties - Molecular Modelling - page 16

The electrostatic potential at field point r due to a small electric dipole p e at the coordinate
origin turns out to be

1
4πε 0

p e . r
r 3

φ ( r ) = (1.23)

which falls off as 1/ r 2 . It falls off faster with r than the potential due to a point charge
because of the cancellation due to plus and minus charges. This is in fact a general rule: the
electrostatic potential for a small electric multipole of order l falls off as r − ( l + 1) so dipole
moment potentials fall off faster than those due to point charges, and so on.

1.11 Polarization and Polarizability

In electrical circuits, charges are stored in capacitors, which at their simplest consist of a
pair of conductors carrying equal and opposite charges. Michael Faraday (1837) made a
great discovery when he observed that filling the space between the plates of a parallel
plate capacitor with substances such as mica increased their ability to store charge. The
multiplicative factor is called the relative permittivity and is given a symbol ε r , as discussed
above. I also told you that the older name is the dielectric constant.
Materials such as glass and mica differ from substances such as copper wire, in that they
have few conduction electrons and so make poor conductors of electric current. We call
materials such as glass and mica dielectrics , to distinguish them from metallic conductors.
Figure 1.12 shows a two-dimensional picture of a dielectric material, illustrated as
positively charged nuclei each surrounded by a localized electron cloud.

Figure 1.12 Dielectric slab

We now apply an electrostatic field, directed from the left to the right. There is a force on
each charge, and the positive charges are displaced to the right whilst the negative charges
move a corresponding distance to the left, as shown in Figure 1.13.
The macroscopic theory of this phenomenon is referred to as dielectric polarization , and
we focus on the induced dipole moment d p e per differential volume dτ . Because it is a
macroscopic theory, no attention is paid to atomic details; we assume that there are a large
number of atoms or molecules within the volume element dτ (or that the effects caused by
the discrete particles have somehow been averaged out).