Week 1: Discrete Charge and the Electrostatic Field 35
charge, to another, leaving behind a surplus of the other sign. Unfortunately, he misguessed the sign
of the mobile charge, thinking it to be the one that he named positive,but as it happens mobile
charge in solid conductors is almost always electrons, which are negative. In 1756 Franklin was
elected as a Fellow of the Royal Society, which in some ways was the “heart” of the Enlightenment,
and remained engaged in natural philsophy (as science was then called) for most of the rest of his
life, but his energies from then on were largely diverted to politics.
Many people felt strongly that electric charge would follow the inverse square law Newton guessed
and then demonstrated for the gravitational field (possibly influenced by other contemporary re-
searchers in the late 17th century). However, only Coulomb, the inventor of a very sensitivetor-
sional balance, was able to use the balance and his ability to precisely divide charges to precisely
demonstrate the correctness of the inverse square law hypothesis and make electrostatics quantita-
tive.
The primary way one can use charge generated by any of several simple electrostatic generators
create conducting objects with at least controlled increments of charge upon them is byinductionand
charge transferorcharge sharing. We will discuss these in more detail next week after establishing
the electrostatic properties of conductors.
Charge, as we shall see, is the fundamental quantity that permitsobjects to “couple” – affect
one another – via the electromagnetic interaction. It therefore will serve use well to know a some of
the most important True Facts about charge.
Experimentally, objects can carry a (net) chargeqwhen “electrified” various ways (for example by
rubbing materials together). Charge comes in two flavors, + and -,but most matter is approximately
charge-neutral most of the time. Consequently, as Benjamin Franklin observed, most charged objects
end up that way by adding or taking away charge from this neutral base. The SI unit of charge is
called theCoulomb(C).
“Like” charges exert a long range (action at a distance) repulsive force on one another. “Unlike”
charges attract. The force varies with the inverse square of thedistance between the charges and acts
along a line connecting them. Coulomb’s Law (covered next) describes this attraction or repulsion
in extremely precise terms.
A quantity that is a constant througout all known interactions, neither created nor destroyed, is
said (in physics) to be “conserved”. In the first semester of this course, you learned of a number of
quantities that wereconditionallyconserved – momentum or angular momentum, conserved when
the net force or torque acting on a system is zero – orunconditionallyconserved, such as net energy
(or more properly, mass-energy).Netcharge is an unconditionally conserved quantity in nature – we
havenever observed an interaction that led to the creation or destruction of net charge^26. Later we
will learn to write this conservation law mathematically in terms of theflux of the current density,
but since we do haven’t yet covered the mathematical tools to do this with, we will for now learn
the experimental result that charge cannot be created nor destroyed; we can only move charge that
already exists from one place to another.
Experimentally, we can readily see that charge can be moved aroundin very large to extremely
small quantities. A natural question is then: Can we continue dividingcharge indefinitely, and move
aninfinitesimalamount of charge? Is charge acontinuousquantity, the way we classically imagine
space and time to be? In Franklin’s time it appeared so, and he spoke of it as being a “fluid” that
could be moved around in arbitrary amounts.
(^26) Later in the study of physics you may learn of interactions that lead to e.g.pair production(or annihilation) – the
simultaneous creation (destruction) of a positron-electron pair, for example. Note well that while charges are indeed
produced (destroyed) in this sort of interaction, the totalcharge of a produced (destroyed) pair iszero, justifying the
careful use of the term “net” in the law. At the “everyday” energies of normal matter at normal temperatures and
absent antimatter, one pretty much can ignore this sort of thing and charge isindividuallyconserved at the discrete
particle level.