It is that time of the semester where we cover Gauss' law and one of
the standard examples is an infinite wire. What is the most compact
nomenclature for the relevant symmetry?
In other words, I want to say that the volume charge density is a
function only of r and not of theta or z.
not a function of theta = cylindrically symmetric*
not a function of z = ???
Looking in many texts, what they do is say the "linear charge density
is constant." I guess that's fine although I then have to digress to
explain why this implies that the volume charge density is not a
function of z.
"Inversion symmetry" might work if I separately said it was
"infinitely long" but this also requires some digression and lacks
compactness.
Carl
*What, if anything, is the distinction between cylindrical, axial,
and azimuthal symmetry? In your reply, consider the following three
shapes for instance:
(a) an infinitely long, straight, constant-diameter piece of spaghetti
(b) a finite-length, straight, constant-diameter piece of spaghetti
(c) an infinitely long, straight piece of spaghetti whose diameter
varies sinusoidally with distance along its axis
--
Dr. Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Annapolis, MD 21402-5026 mailto:mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/