Electric Charge

You are certainly familiar with electronic devices that you activate with the click of a switch,
from computers to cell phones to television. And you have certainly seen electricity in a
flash of lightning during a heavy thunderstorm. But you have also most likely experienced
electrical effects in other ways, maybe without realizing that an electric force was involved.
Let’s take a look at some of these activities and see what we can learn from them about
electric charges and forces.

Discoveries
You have probably experienced the phenomenon of static electricity: When you first take
clothes out of a dryer, many (not all) of them tend to stick together; for some fabrics, they
can be very difficult to separate. Another example occurs if you take a woolen sweater off
quickly—you can feel (and hear) the static electricity pulling on your clothes, and perhaps
even your hair. If you comb your hair on a dry day and then put the comb close to a thin
stream of water coming out of a faucet, you will find that the water stream bends toward (is
attracted to) the comb.

An electrically charged comb attracts a stream of water from a distance. Note that the water
is not touching the comb. (credit: Jane Whitney)
Suppose you bring the comb close to some small strips of paper; the strips of paper are
attracted to the comb and even cling to it. In the kitchen, quickly pull a length of plastic
cling wrap off the roll; it will tend to cling to most any nonmetallic material (such as plastic,
glass, or food). If you rub a balloon on a wall for a few seconds, it will stick to the wall.
Probably the most annoying effect of static electricity is getting shocked by a doorknob (or
a friend) after shuffling your feet on some type of carpeting.
 After being used to comb hair, this comb attracts small strips of paper from a distance,
without physical contact. Investigation of this behavior helped lead to the concept of the
electric force. (credit: Jane Whitney)
Many of these phenomena have been known for centuries. The ancient Greek philosopher
Thales of Miletus (624–546 BCE) recorded that when amber (a hard, translucent, fossilized
resin from extinct trees) was vigorously rubbed with a piece of fur, a force was created that
caused the fur and the amber to be attracted to each other. Additionally, he found that the
rubbed amber would not only attract the fur, and the fur attract the amber, but they both
could affect other (nonmetallic) objects, even if not in contact with those objects.
Borneo amber is mined in Sabah, Malaysia, from shale-sandstone-mudstone veins. When a
piece of amber is rubbed with a piece of fur, the amber gains more electrons, giving it a net
negative charge. At the same time, the fur, having lost electrons, becomes positively
charged. (credit: “Sebakoamber”/Wikimedia Commons)

When materials are rubbed together, charges can be separated, particularly if one material
has a greater affinity for electrons than another. (a) Both the amber and cloth are originally
neutral, with equal positive and negative charges. Only a tiny fraction of the charges are
involved, and only a few of them are shown here. (b) When rubbed together, some negative
charge is transferred to the amber, leaving the cloth with a net positive charge. (c) When
separated, the amber and cloth now have net charges, but the absolute value of the net
positive and negative charges will be equal.
The English physicist William Gilbert (1544–1603) also studied this attractive force, using
various substances. He worked with amber, and, in addition, he experimented with rock
crystal and various precious and semi-precious gemstones. He also experimented with
several metals. He found that the metals never exhibited this force, whereas the minerals
did. Moreover, although an electrified amber rod would attract a piece of fur, it would repel
another electrified amber rod; similarly, two electrified pieces of fur would repel each other.
This suggested there were two types of electric property; this property eventually came to
be called electric charge. The difference between the two types of electric charge is in the
direction of the electric forces that each type of charge causes: These forces are repulsive
when the same type of charge exists on two interacting objects and attractive when the
charges are of opposite types. The SI unit of electric charge is the coulomb (C), after the
French physicist Charles-Augustin de Coulomb (1736–1806).
The most peculiar aspect of this new force is that it does not require physical contact
between the two objects in order to cause an acceleration. This is an example of a so-called
“long-range” force. (Or, as James Clerk Maxwell later phrased it, “action at a distance.”) With
the exception of gravity, all other forces we have discussed so far act only when the two
interacting objects actually touch.
The American physicist and statesman Benjamin Franklin found that he could concentrate
charge in a “Leyden jar,” which was essentially a glass jar with two sheets of metal foil, one
inside and one outside, with the glass between them. This created a large electric force
between the two foil sheets.

A Leyden jar (an early version of what is now called a capacitor) allowed experimenters to
store large amounts of electric charge. Benjamin Franklin used such a jar to demonstrate
that lightning behaved exactly like the electricity he got from the equipment in his
laboratory.
Franklin pointed out that the observed behavior could be explained by supposing that one
of the two types of charge remained motionless, while the other type of charge flowed from
one piece of foil to the other. He further suggested that an excess of what he called this
“electrical fluid” be called “positive electricity” and the deficiency of it be called “negative
electricity.” His suggestion, with some minor modifications, is the model we use today.
(With the experiments that he was able to do, this was a pure guess; he had no way of
actually determining the sign of the moving charge. Unfortunately, he guessed wrong; we
now know that the charges that flow are the ones Franklin labeled negative, and the
positive charges remain largely motionless. Fortunately, as we’ll see, it makes no practical
or theoretical difference which choice we make, as long as we stay consistent with our
choice.)
Let’s list the specific observations that we have of this electric force:
• The force acts without physical contact between the two objects.
• The force can be either attractive or repulsive: If two interacting objects carry the
same sign of charge, the force is repulsive; if the charges are of opposite sign, the
force is attractive. These interactions are referred to as electrostatic repulsion and
electrostatic attraction, respectively.
• Not all objects are affected by this force.
• The magnitude of the force decreases (rapidly) with increasing separation distance
between the objects.
To be more precise, we find experimentally that the magnitude of the force decreases as the
square of the distance between the two interacting objects increases. Thus, for example,
when the distance between two interacting objects is doubled, the force between them
decreases to one-fourth what it was in the original system. We can also observe that the
surroundings of the charged objects affect the magnitude of the force. However, we will
explore this issue in a later chapter.

Properties of Electric Charge

In addition to the existence of two types of charge, several other properties of charge have
been discovered.
• Charge is quantized. This means that electric charge comes in discrete amounts,
and there is the smallest possible amount of charge that an object can have. In the SI
−19
system, this smallest amount is 𝑒 ≡ 1. 602 × 10 𝐶. No free particle can have
less charge than this, and, therefore, the charge on any object—the charge on all
objects—must be an integer multiple of this amount. All macroscopic, charged
objects have a charge because electrons have either been added or taken away from
them, resulting in a net charge.
• The magnitude of the charge is independent of the type. Phrased another way,
the smallest possible positive charge (to four significant figures) is
−19
+ 1. 602 × 10 𝐶, and the smallest possible negative charge is
−19
− 1. 602 × 10 𝐶; these values are exactly equal. This is simply how the laws of
physics in our universe turned out.
• Charge is conserved. Charge can neither be created nor destroyed; it can only be
transferred from place to place, from one object to another. Frequently, we speak of
two charges “canceling”; this is verbal shorthand. It means that if two objects that
have equal and opposite charges are physically close to each other, then the
(oppositely directed) forces they apply on some other charged object cancel, for a
net force of zero. You must understand that the charges on the objects by no means
disappear, however. The net charge of the universe is constant.
• Charge is conserved in closed systems. In principle, if a negative charge
disappeared from your lab bench and reappeared on the Moon, the conservation of
charge would still hold. However, this never happens. If the total charge you have in
your local system on your lab bench is changing, there will be a measurable flow of
 charge into or out of the system. Again, charges can and do move around, and their
effects can and do cancel, but the net charge in your local environment (if closed) is
conserved. The last two items are both referred to as the law of conservation of
charge.

The Source of Charges: The Structure of the Atom

Once it became clear that all matter was composed of particles that came to be called
atoms, it also quickly became clear that the constituents of the atom included both
positively charged particles and negatively charged particles. The next question was, what
are the physical properties of those electrically charged particles?
The negatively charged particle was the first one to be discovered. In 1897, the English
physicist J. J. Thomson was studying what was then known as cathode rays. Some years
before, the English physicist William Crookes had shown that these “rays” were negatively
charged, but his experiments were unable to tell any more than that. (The fact that they
carried a negative electric charge was strong evidence that these were not rays at all, but
particles.) Thomson prepared a pure beam of these particles and sent them through
crossed electric and magnetic fields, and adjusted the various field strengths until the net
deflection of the beam was zero. With this experiment, he was able to determine the
charge-to-mass ratio of the particle. This ratio showed that the mass of the particle was
much smaller than that of any other previously known particle—1837 times smaller, in fact.
Eventually, this particle came to be called the electron.
Since the atom as a whole is electrically neutral, the next question was to determine how
the positive and negative charges are distributed within the atom. Thomson himself
imagined that his electrons were embedded within a sort of positively charged paste,
smeared out throughout the volume of the atom. However, in 1908, the New Zealand
physicist Ernest Rutherford showed that the positive charges of the atom existed within a
tiny core—called a nucleus—that took up only a very tiny fraction of the overall volume of
the atom but held over 99% of the mass. In addition, he showed that the negatively charged
electrons perpetually orbited about this nucleus, forming a sort of electrically charged
cloud that surrounds the nucleus. Rutherford concluded that the nucleus was constructed
of small, massive particles that he named protons.
This simplified model of a hydrogen atom shows a positively charged nucleus (consisting, in
the case of hydrogen, of a single proton), surrounded by an electron “cloud.” The charge of
the electron cloud is equal (and opposite in sign) to the charge of the nucleus, but the
electron does not have a definite location in space; hence, its representation here is as a
cloud. Normal macroscopic amounts of matter contain immense numbers of atoms and
molecules, and, hence, even greater numbers of individual negative and positive charges.
Since it was known that different atoms have different masses and that ordinarily atoms are
electrically neutral, it was natural to suppose that different atoms have different numbers of
protons in their nucleus, with an equal number of negatively charged electrons orbiting
about the positively charged nucleus, thus making the atoms overall electrically neutral.
However, it was soon discovered that although the lightest atom, hydrogen, did indeed have
a single proton as its nucleus, the next heaviest atom—helium—has twice the number of
protons (two), but four times the mass of hydrogen.
This mystery was resolved in 1932 by the English physicist James Chadwick, with the
discovery of the neutron. The neutron is, essentially, an electrically neutral twin of the
proton, with no electric charge, but (nearly) identical mass to the proton. The helium
nucleus therefore has two neutrons along with its two protons. (Later experiments were to
show that although the neutron is electrically neutral overall, it does have an internal
charge structure. Furthermore, although the masses of the neutron and the proton are
nearly equal, they aren’t exactly equal: The neutron’s mass is very slightly larger than the
mass of the proton. That slight mass excess turned out to be of great importance. That,
however, is a story that will have to wait until we study modern physics in the next chapter)
Thus, in 1932, the picture of the atom was of a small, massive nucleus constructed of a
combination of protons and neutrons, surrounded by a collection of electrons whose
combined motion formed a sort of negatively charged “cloud” around the nucleus. In an
electrically neutral atom, the total negative charge of the collection of electrons is equal to
the total positive charge in the nucleus. The very low-mass electrons can be more or less
easily removed or added to an atom, changing the net charge on the atom (though without
changing its type). An atom that has had the charge altered in this way is called an ion.
Positive ions have had electrons removed, whereas negative ions have had excess electrons
added. We also use this term to describe molecules that are not electrically neutral.

The nucleus of a carbon atom is composed of six protons and six neutrons. As in hydrogen,
the surrounding six electrons do not have definite locations and so can be considered to be
a sort of cloud surrounding the nucleus.
The story of the atom does not stop there, however. In the latter part of the twentieth
century, many more subatomic particles were discovered in the nucleus of the atom: pions,
neutrinos, and quarks, among others. Except for the photon, none of these particles are
directly relevant to the study of electromagnetism, so we defer further discussion of them
until the chapter on particle physics.

A Note on Terminology
As noted previously, electric charge is a property that an object can have. This is similar to
how an object can have a property that we call mass, a property that we call density, a
property that we call temperature, and so on. Technically, we should always say something
like, “Suppose we have a particle that carries a charge of 3 µ𝐶.” However, it is very common
to say instead, “Suppose we have a 3 − µ𝐶 charge.” Similarly, we often say something like,
“Six charges are located at the vertices of a regular hexagon.” A charge is not a particle;
rather, it is a property of a particle. Nevertheless, this terminology is extremely common. So,
keep in the back of your mind what we mean when we refer to a “charge.”