phy1020.DVI

15.2 Coulomb’s Law

Using a torsion balance, the 18th century French physicist Charles-Augustin de Coulomb discovered the
law that determines the amount of force between two charged bodies—a law now calledCoulomb’s law.It
states that if two point chargesq 1 andq 2 are separated by a distancer, then the force between them will be
proportional to the product of the charges and inversely proportional to the square of the distance between
them:

FD

1

4" 0

q 1 q 2

r^2

: (15.1)

HereFis the force (in newtons),ris the separation distance (meters), andq 1 andq 2 are the charges measured
in units ofcoulombs(C). A coulomb is a very large unit of charge; charges we encounter in the laboratory
will typically be on the order of microcoulombs (C) or nanocoulombs (nC).
The constant" 0 in Eq. (15.1) is called thepermittivity of free space,^1 and is equal to^2

" 0 D8:85418781762038985::: 10 ^12 C^2 N^1 m^2 : (15.2)

The proportionality constant1=.4" 0 /is called theCoulomb constant(kc). It is equal to exactly

kcD

1

4" 0

D8:9875517873681764 109 Nm^2 C^2 : (15.3)

Coulomb’s law (Eq. 15.1) implicitly makes use of a property in arithmetic that mirrors the properties of
electric charges. Multiplying two numbers of like sign gives a positive number, and multiplying two numbers
of unlike sign gives a negative number. This property mirrors the behavior of electric charges: two charges
of like sign repel, and two charges of unlike sign attract. So in Coulomb’s law (Eq. (15.1)), we can interpret
apositiveforce as repulsion, and anegativeforce as attraction.

15.3 Atomic View of Electricity.

As you will have already learned, all ordinary matter consists ofatoms. At the center of the atom is a tiny,
massivenucleus, which is surrounded by shells of very lightelectrons. The nucleus consists of electrically
neutral (uncharged)neutronsalong with positively-chargedprotonsthat carry a charge equal to the elementary
charge,eD1:6021766208 10 ^19 C. The electrons surrounding the nucleus carry anegativecharge, also
equal to the elementary charge. In other words, neutrons have charge 0, protons have chargeCe, and electrons
have chargee.
In ordinary matter, it is only theelectronsthat move around and produce electric charge and electric
currents. The protons are massive (about 1800 times heavier than the electrons) and tucked away in the
center of the atom, so they barely move. When we rub a piece of amber with a piece of fur, for example,
we’re removing a small number of the outermost electrons from atoms in the fur, and depositing them onto
the amber. This leaves the fur with a deficiency of electrons (giving it a positive charge) and the amber with
extra electrons (giving it a negative charge). Very few electrons are involved in this type of charging: if only
one fur atom in aquintillionloses an electron to the amber, it will produce an easily measurable electric
charge, enough to allow the amber to pick up bits of paper, for example.
So keep this in mind: whenever you’re charging objects or creating electric currents in the laboratory, it
is always the negatively-chargedelectronsthat are moving.^3

(^1) " 0 is pronounced “epsilon-nought.”
(^2) Because of the way SI units are defined, the constant" 0 is a transcendental number that may be computed to as many digits as
desired; its exact value is1=.299792458^2 4 10 ^7 /C^2 N^1 m^2.
(^3) Two hydrogen atoms walk into a bar. One says, “I’ve lost my electron.” The other says, “Are you sure?” The first replies, “Yes, I’m
positive...”