Week 8: Faraday’s Law and Induction 289
We don’t have to go to the extreme case of superconductivity to require a bit of quantum theory in
our explanation, however. Basically all three of the primary ways ordinary matter modifies magnetic
fields are at least partially quantum mechanical in their explanation.
Atoms can be thought of as more or less spherically symmetric balls ofelectrons surrounding
heavy pointlike nuclei. The electrons are in “orbits” around these nuclei, but the orbits are not
classical orbits like the Moon orbiting the Earth, they are non-radiating, zero resistance flows of
electronic current around the nucleus.
If a magnetic field is increased in the vicinity of an atom, Faraday’s Lawsuggests that all elec-
tronic currents around an axis parallel to the magnetic field through the nucleus will be increased or
decreased as needed in order toreducethat field. This alteration in the currents can be accompanied
by an increase or decrease in the average radius of the orbits in question, and by small changes in
the energy of those orbits.
If the currents wereclassical currents moving against some form of resistance, the decrease
in magnetic field strength due to the induced current would be small, transient and difficult to
detect. However, quantum atomic orbitals haveno resistance. As long as the external magnetic
field isn’t variedtoorapidly bytoogreat an amount, so that the atom has time to “smoothly”
adjust its orbitals, the induced current variation doesn’t involve dissipation and the field reduction
dynamically tracks the applied field and is “permanent”.
To see what happens inside a block of dense matter, we need to consider how all of these reactive
currents combine. In figure 107 an external magnetic field into thepage is applied to a (highly
Internal current cancelsNet surface currentSurface current does notApplied External Magnetic Field (out of page)Figure 107: Wherever “atomic” magnetic current loops adjoin one another, the average current is
zero. On the surface, however, there are no neighboring atoms,and the current loops there are not
cancelled. They add (on average) into acontinuous surface currentnot unlike that of a solenoid, so
that the field everywhere in the interior isreduced.
magnified) block of material. This field induces non-dissipating atomic currents in the atoms that
create magnetic dipoles pointingintothe page.
Inside the bulk of the material, the current circulating around one atom approximately cancels
the current circulating around the atoms next to it, where they are in contact. If one does a coarse
grained average of the current, it is nearly zero in any small volume of the material containing many
atoms.
This is not true on the surface. The currents of the atoms on the surface have no neighboring
atoms with currents running the opposite way on the outside, so there the currents allcombine, on