290 Week 8: Faraday’s Law and Induction
average, to produce a net current running around the perimeterof the object. This current is almost
identical to that of asolenoid, and, like a solenoid, there is a uniform field inside the material that
directly opposes the applied external field and hence reduces it inside of the material^79.
We will call this reactive responsediamagnetism, the exact analog of the dielectric response
of most insulators and conductors. Nearly all materials have a diamagnetic response to applied
magnetic fields (especially at higher temperatures), but many materials have this response overridden
by one or both of the following kinds of bulk magnetization, which havevery different explanations.
Superconductors
Certain materials, when cooled to extremely low absolute temperatures, becomesuperconductors.
Superconductivity is a more or less purely quantum mechanical phenomenon and hence is beyond
the scope of this book – basically a fraction of the electronic chargestarts to behave collectively like
a macroscopic quantum “orbital” that can transport electronic charge without resistance.
Superconductors can be thought of as being “diamagnetic” – indeedperfectlydiamagnetic (as
well as being perfectly dielectric) as they tolerate no magnetic or electric field inside at all, but it
isn’t exactly the same mechanism as merely opposing an applied field via induction; a superconduc-
tor activelyejectsany existing magnetic field as it is cooled across the transition temperature where
superconductivity appears, even if that field is not changing. One visible sign of this ejection is that
superconductors placed above a permanent magnetfloat, suspended by its perfectly opposed mag-
netic field. This is called the Wikipedia: http://www.wikipedia.org/wiki/Meissner EffectMeissner
Effect.
Superconductors, of course, are potentially very useful – a longterm search continues for finding
specially engineered materials that are superconducting at e.g. room temperature. A room tem-
perature superconductor would have enormous positive implications for our civilization – levitating
trains that require no energy to levitate, loss-free transmission of electrical energy over long dis-
tances, and much more – but so far they have eluded our search. As of the time of this writing,
the highest temperature superconductors thus far found havecritical temperatures in the range of
100-150 degrees Kelvin, over 100 degrees Kelvin short of even thefreezing point of water.
Still, enormous progress has been made in recent decades. We can certainly at least hope that
high(er) temperature superconductors eventually have a significant impact on our lives.
Paramagnetism
Some molecules have permanent electric dipole moments.Manyatoms or molecules have permanent
magneticdipole moments. This is a purely quantum mechanical phenomenon. Charged electrons
and protons havespinand hencearepermanent magnetic dipoles. As atoms and nuclei are “built”
out of many protons, neutrons, and electrons these spins are paired when possible in such a way
that no net moment results, but all across the periodic table are elements with unpaired electrons or
protons, and at least potential net spin and magnetic moment. Thisangular momentum combines
with orbital angular momentum to produce many atoms with magneticdipole moments^80.
We know that magnetic dipoles have a potential energy in an applied magnetic field that is a
minimumwhen the dipoles are aligned with the field. Although (as we have seen)magnetic dipoles
associated with angular momentum on the scale of elementary particles or atoms experience a torque
(^79) This follows from Ampere’s Law applied to e.g. paths parallel to the applied field on the inside of the material
that contain a piece of the surface current, similar to the “infinite plane sheet of current” we considered earlier.
(^80) Wikipedia: http://www.wikipedia.org/wiki/Magneticmoment#Magneticmomentofanatom. In fact there is a
dizzying array of ways these moments can arise, too many to exhaustively and correctly cover here.