288 Week 8: Faraday’s Law and Induction
Magnetic brakes can use this same principle to stop a car, although (as a homework problem will
demonstrate) one can avoid wasting the energy by turning the wheel rotors into “generators” that
can store the energy in a battery as they remove it.
We will return to the notion of eddy currents when we treat transformers because the iron cores of
transformers are usuallylaminated– made of thin sheets or wires of iron coated with and separated
by an insulating resin – precisely to prevent eddy currents from therapidly changing magnetic fields
they help support from heating the iron and hence wasting theenergyin the time varying magnetic
field.
8.11: Magnetic Materials
We have postponed discussing the magnetic properties of materialsuntil here because we had to wait
until we understood the basic idea of Faraday’s and Lenz’s Laws. Aswe will see, thediamagnetic
property of some materials that corresponds to thedielectricproperties we’ve already studied comes
about as a result of Faraday’s Law.
However, another good reason to wait until now is thatmagnetic properties of materials are much
more complicatedthan electrical properties were. Back in electrostatics, dielectricpolarization was
about it. Well, not really – a veryfewmaterials exhibit e.g. ferroelectric properties, and further
study also reveals that dielectric polarization and electrical conductivity are two aspects of a single
complex quantity and not really independent – but close enough. If you put nearly any material in
a static or slowly varying electrical field, the field inside that materialwill bereduced.
If you put thatsamematerial in a static or slowly varying electrical field, you might find:- The magnetic field inside isreduced. We call thisdiamagnetism.
- The magnetic field inside isincreased. We call thisparamagnetism.
- The magnetic field is altered by the addition of another vector magnetic field produced by the
material itself, a field that persists even if there isnoexternal field. We call thisferromag-
netism.
These are all bulk descriptions, and fail to capture the wide varietyof magnetic structure one
can discover on the microscopic scale of the material. They also are all properties that depend
on thetemperatureof the material. In fact, a single material can, at different temperatures, be
ferromagnetic, paramagnetic, and diamagnetic!
Thus far, we have been pretty successful in understanding things classically, but certain aspects
of the magnetic properties of matter rely heavily on quantum mechanics, in particular the fact that
electrons havespin(and hence an intrinsic magnetic dipole moment) andorbit the atomic nucleus
in non-radiating, non-resistive orbits. We will have to draw at least on these “cartoon” ideas as we
seek to grasp the general concepts and ideas underlying magneticbehavior of materials.
Diamagnetism
This is a course on classical physics, but magnetism in particular is very difficult to understand on
purely classical grounds. For example, we’ve seen above how conductors will at least transiently
reducemagnetic fields that attempt to penetrate them, as eddy currents are induced around their
perimeter. We can imagine that a superconductor withzeroresistance would reduce those fields to
zero (and indeed that is the oversimplified case, with some limitations)but superconductivity is a
purely quantum phenonmenon.