38 Week 1: Discrete Charge and the Electrostatic Field
molecule to the next by small electric fields. We say that theseconduction electronsarefreeto
move in response to applied field and that the materialconducts electricity. Conductors also
have some special properties when they respond to applied fields beyond this that we’ll learn
about later. Since electrons are bound to atoms by forces with a finite magnitude,all matter
is a conductor in a strong enough field. Dielectric insulators that areplaced in such a strong
field experience something calleddielectric breakdownand shift suddenly from an insulating
to a conducting state. Lightning is a spectacular example of dielectric breakdown.- Semiconductors. These are materials that can be shifted between being a conductor or an
insulator depending on the potential difference at the interfaces between different “kinds” of
semiconducting materials. This is an entirely quantum mechanical effect and his hence a bit
beyond the classical bounds of this course, but it certainly doesn’thurt to know that they
exist, as semiconductors areextremely importantto our society. In particular, semiconductors
are used in three critical ways: they are used to make diodes (whichwe will indeed study when
we talk of rectification in AM radios), as amplifiers (transistors) (used to make the music
adjustably loud enough to listen to), and asswitchesfrom which the digital information pro-
cessing devices are built that dominate modern existence. This list is far from exhaustive – see
Wikipedia: http://www.wikipedia.org/wiki/semiconductors for a more complete discussion.
From this you can see that charge is indeed ubiquitous. We (and everything around us) are made
up of charged particles – even the neutral neutrons in the nuclei that make up most of our mass are
made up of charged particles. What holds atoms together? What keeps atoms apart? It is time
to learn about one of the most important force laws in the Universe,the one that is perhaps most
responsible for chemistry and biology.
1.2: Coulomb’s Law
Coulomb’s Law is very simple. If one charges various objects (for example, two conducting balls
suspended from an insulating string so that they are near to one another but not touching) and
measures the deflection of the string when the balls are in force equilibrium, one can verify that:
- The force between the charges is proportional to each charge separately. The force isbilinear
in the charge. - The force acts along the line connecting the two charges.
- The force is repulsive if the charges have the same sign, attractiveif they have different signs.
- The force is inversely proportional to the square of the distance between them.
These four experimental observations are summarized asCoulomb’s Law. They are a law of
nature, on a par with Newton’s Law of Gravitation (which it greatly resembles), although we will
actually use anequivalent(and slightly more fundamental) version of this law, Gauss’s Law for
Electrostatics, as the version we will spend most of our time studying.
In general, while we like to understand laws like this verbally, they are moreusefulto us if we
can formulate themalgebraically. We therefore write the force actingoncharge 1due tocharge 2
as:
F~ 12 =keq 1 q 2 (~r^1 −~r^2 )
|~r 1 −~r 2 |^3(1)
Note that it acts on a linefromcharge 2tocharge 1, is proportional to both charges, is inversely
proportional to the distance that separates them squared, andis repulsive if both charges have the