You should now be familiar with the long integral mathematical form of Faraday's Law of magnetic induction: in SI units,
Suppose we get annoyed at the complexity of this formula and
decide to shrink the loop
and its enclosed area
down to an infinitesimal point;
then we no longer have to worry about macroscopic changes in
or
but can reduce
the problem to differentials.
Without showing a detailed derivation,
I will merely state that the circulation per unit area
can be expressed in terms of the curl of
and ``it can be shown'' that the integral equation
above is completely equivalent to the
differential form of Faraday's Law,
which describes part of the behaviour of electric and magnetic
fields at every point in space:
This says, in essence, that any change in the magnetic field with time induces an electric field perpendicular to the changing magnetic field.
Hold that thought.