15.4 Materials.
Different materials behave differently depending on their ability to allow electrons to flow through them. We
classify materials as follows:
- Conductorsare materials in which electrons can flow very easily. You can think of a conductor as a
lattice of positive ions, surrounded by a kind of “gas” of free electrons that belong to no particular
atom. The free electrons are free to move throughout the conductor. Familiar conductors are metals
such as copper, gold, and silver. - Insulators(ordielectrics) are materials in which each atom holds on to all of its atoms strongly, so
they arenotfree to move through the material. Examples of insulators are rubber, wood, plastics, and
ceramics. - Semiconductorsare between conductors and insulators. They are insulators that can be coaxed into
giving up a conduction electron under the right conditions, such as a sufficiently strong electric field.
Common semiconductors are the elements silicon and germanium. - Superconductorsare exotic materials that form a special class of conductor. While ordinary conductors
always offer some sort of resistance to the flow of electrons, superconductors offer no such resistance.
This means, for example, that if you form a superconductor into a ring and start electrons flowing in
it, they will continue flowing forever. Traditional superconductors are made by cooling an ordinary
conductor like mercury down to very low temperatures; below some critical temperature, the material
will suddenly transition from an ordinary conductor to a superconductor. Experiments in the 1980s
discovered a new class of superconductors calledhigh-temperature superconductorsthat are made of
exotic ceramic-like materials. These still need to be cooled to become superconducting, but not nearly
as much. For example, mercury doesn’t become superconducting until it’s cooled down to 4.1 K, which
requires liquid helium temperatures and is difficult to do. But the high-temperature superconductor
YBa 2 Cu 3 O 7 only needs to be cooled to 90 K, which can easily be achieved by cooling with liquid
nitrogen.
An exotic form of hydrogen calledmetallic hydrogenis thought to exist at the very high pressures (more
than 4 million atmospheres) in the interior of the planets Jupiter and Saturn. Scientists are currently
attempting to create metallic hydrogen in the laboratory, so far without success. Metallic hydrogen is
thought to be either a solid or a superfluid^4 , and theory suggests it may possibly be a room-temperature
superconductor. Its creation in the laboratory could have significant commercial applications.
15.5 Coulomb’s Law in Two or Three Dimensions
Coulomb’s law in the form shown in Eq. (15.1) works fine for a one-dimensional problem involving two
point charges: the sign of the forceFis sufficient to indicate the direction of the force. But when we work
in two or three dimensions (for example, point charges on the vertices of a triangle) we must usevectorsto
determine the force in each charge. In vector form, Coulomb’s law is
F 12 D
1
4" 0
q 1 q 2
r^2rO 12 ; (15.4)whereF 12 is the force on chargeq 1 due to chargeq 2 , andrO 12 is aunit vector(a vector of magnitude 1) that
points in the direction from chargeq 1 to chargeq 2. Note the minus sign: if both charges are positive, for
example, then the force pointsoppositerO 12 —that is, the force onq 1 will be away fromq 2.
(^4) See chapter 59.