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
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:
Now we're getting somewhere.