Week 1: Discrete Charge and the Electrostatic Field 47
require a calculator to evaluate.
1.5: Electric Dipoles
As we just noted, the arrangement of two equal but opposite charges above is called anelectric
dipole^30 , and dipole fields play an enormously important role in physics. That is because dipolar
arrangements of charge arecommonin nature. Let’s see why.
+e−e
+e−eEFigure 7: An atom in an electric fieldpolarizesas its nucleus is displaced relative to its electron cloud.
We will work with a very simplemodelfor an atom called theLorentz Oscillator Modelthat idealizes
an atom as a uniform ball of negative charge symmetrically surrounding a small massive positively
charged nucleus (such that the total charge is zero). This modelworks well all the way up tograduate
electrodynamics to help students understand the general principles of dielectric polarization!
A simple model for an atom has a nucleus symmetrically surrounded bya spherical ball of charge
in such a way that the result is electrically neutral and produces (aswe shall see) no electric field
outside the atom. If such an atom is placed in an electric field, the nucleus is pulled one way and the
electron cloud is pushed the other way, and while the atom remains electrically neutral the vector
fields produced by the positive and negative charges are symmetricabout different centers andno
longer precisely cancel.
In a few weeks we will consider the field produced by the polarized atomson average inside
a solid as this fieldmodifiesthe field that polarizes the atoms and we will learn some wonderful
things, such as the fact that the natural motion of the charge distribution in this idealized model is
toharmonically oscillate(hence its name: theLorentz Oscillator Model.
For the moment, however, it suffices for us to recognize that sincewearea big pile of atoms and
those atoms spontaneously polarize in electrical fields (which are also ubiquitous), the forces and
torques acting on dipoles, and the fields produced by dipoles, are both of great interest to us as we
seek to understand ourselves and everyday “stuff” about the world around us such as why charged
balloons stick to walls, why the sky is blue and the sunset is red, why matter hangstogethereven
though it is generally electrically neutral – some stuff that seems merely interesting and other stuff
that seems as though it might be very important indeed in our effortsto build a rational worldview
that explains the world of our everyday experience in simple, intuitiveterms.
We will therefore start by modelling the resulting charge distributionof a polarized atom (or any
other dipolar system) as a basic electric dipole constructed directlyout of two pointlike charges of
opposite sign separated by a vector distance~lfrom the negative to the positive charge:
When two electric charges of equal magnitude and opposite sign arebound together, they form
anelectric dipole. To understand the properties of dipoles as “objects”, we will initially presume
them to be bound together with a “rigid rod” of some sort so the dipole moment itselfdoesn’t
(^30) Wikipedia: http://www.wikipedia.org/wiki/dipole.