You are probably also adept at using
the trick developed by Henri Ampère for calculating
the magnetic field
(
)
due to various symmetrical arrangements of
electric current (*I*).
In its integral form and SI units, AMPÈRE'S LAW reads

where Maxwell's " DISPLACEMENT CURRENT" associated with a time-varying electric displacement has been included. This equation says (sort of), "The

As you know, this "Law" is used with various
symmetry arguments to "finesse" the evaluation of magnetic
fields due to arrangements of electric currents,
much as GAUSS' LAW was used to calculate
electric fields due to different arrangements of
electric charges. Skipping over the details, let me
draw your attention to the formal similarity to FARADAY'S LAW
and state (this time without showing the derivation) that
there is an analogous
*differential form* of AMPÈRE'S LAW describing
the behaviour of the fields at any point in space:

If we ignore the current density then this equation says (sort of), "

Now we're getting somewhere.

Jess H. Brewer - Last modified: Wed Nov 18 12:32:15 PST 2015