Physics 2140 Notes
Introduction
In mechanics, we discussed a number of types of forces: for example, normal, tension, and
friction. There is also gravity, but gravity is different from the others, because it is a noncontact force: the Earth does not need to be touching an object (like you, or the moon) to
exert a gravitational force on it. Gravity was the only noncontact force we have studied so
far, but in this class we will introduce two other noncontact forces: the electric and
magnetic forces. Electromagnetic forces, as they are collectively referred to, are very
pervasive: except for gravity and a couple other exceptions, all interactions between
objects occur due to the electromagnetic forces, which hold atoms and molecules
together.
In this class we will start by discussing static electricity, followed by current, and
magnetism. We will end with optics, because light arises from a complex interaction of
electric and magnetic forces.
Electric Charge
There are two types of electric charge: positive and negative. The proton and the electron
are examples of each. Protons and electrons have equal but opposite charge, so that a
hydrogen atom, which consists of a proton and an electron, is neutral or uncharged. (This
is actually rather surprising, because protons and electrons are otherwise very different.)
All charge we see in everyday life is due to protons and electrons: positively charged
objects have an excess of protons (or a lack of electrons), and negatively charged objects
have an excess of electrons (or a lack of protons).
e–
Na
Cl
Na+
Cl–
11 protons
11 electrons
17 protons
17 electrons
11 protons
10 electrons
17 protons
18 electrons
Consider an example from chemistry: typically, a sodium atom has 11 protons and 11
electrons, and so is neutral; likewise, the chlorine atom has 17 of each. When a sodium
atom approaches a chlorine atom, an electron typically jumps from the sodium atom to
the chlorine atom; this makes the sodium atom a positive ion and the chlorine atom a
negative ion. The sodium and chlorine ions then attract one another, because they are
oppositely charged: two objects of opposite charge attract one another, while objects of
like charge (like two positive sodium ions) repel one another.
Charged objects of both types also attract neutral objects. To explain why this should be
so, we first need to discuss the difference between conductors and insulators. The atoms
of both consist of positive nuclei surrounded by a negatively charged cloud of electrons.
In some materials, called insulators, all the electrons are held tightly to their nuclei, unable
In the atoms of an insulator, electrons
are held tight to their positive nuclei.
In the atoms of a conductor, some
electrons are allowed to roam free.
to move very far. In a conductor, however, one or more electrons of each atom can roam
freely throughout the material, forming a “sea” of electrons which can respond to external
stimuli.
For example, if you place an electron on one end of an insulating rod, that end becomes
Place an electron
on one end
Shift electrons from
one end to the other
e–
Insulators:
e–
Conductors:
e–
e–
negatively charged, but the remainder of the rod remains neutral. In a conductor,
however, the free electrons are repelled by the additional electron, and so shift to the right,
until the entire rod is negatively charged: thus charge remains localized on insulators but
distributes itself evenly in a conductor. If we connect the rods to a battery, it removes
electrons from one end of the rod and dumps them onto the other end. In an insulator, all
this does is create a negative buildup of charge on one end, and a positive charge on the
other. In a conductor, however, the free electrons are set into motion, and so current
(moving charge) is set up in the rod. Conductors are thus materials, like metals, which
allow electricity to flow through them; while insulators are materials like wood, plastic, or
glass.
conductor
conductor
Now suppose we place a positively charged rod next to a neutral conductor. The free
electrons are attracted by the positive rod, and drift to the left. The left side becomes
negative, and this pulls the sphere to the left. The right side becomes positive due to the
lack of electrons over there, and this pushes the sphere to the right. However, electric
forces decay over distance, so the attraction due to the negative charge is stronger than the
repulsion due to the positive charge, and so the neutral sphere is attracted to the rod.
Similarly, a negative rod pushes the electrons to the right-hand side, and the sphere is still
attracted to the charge again. We say that the sphere has become polarized, with opposite
charges on opposite sides of the sphere.
Technically speaking, inside a conductor it is the electrons which move about; the positive
charge remains still. We call these electrons charge carriers. In theory, however, we can
pretend as if the conductor contains both positive and negative charge carriers, which can
both move in the appropriate directions. There may also be certain circumstances when
we will pretend that the charge carriers are entirely positive (as in a current-carrying wire,
for instance). Mathematically, there are few instances where the identity of the charge
carrier matters, and none which we will discuss in this class (unless I explicitly mention it).
atom
insulator
We’ve seen how conductors can become polarized due to the drift of charge. However,
insulators can become polarized as well, but at the atomic level. When an atom is placed
next to a positively charged rod, the electron cloud of the atom is pulled slightly to the left,
causing the atom to be polarized. When the same rod is placed next to an insulator, all its
atoms become polarized, and this creates a layer of negative charges along the left-hand
side, as seen in the figure, and a layer of positive charges along the right-hand side, just as
with the conductor. Thus insulators are attracted to charged objects as well.