A variable used in → spherical harmonic expansions.
Each spherical harmonic is characterized by its multipole index l:
l = 0 for a → monopole,
l = 1 for a → dipole,
and so on. It is used in particular to describe the
→ cosmic microwave background anisotropy:
ΔT/T_{0} (θ,φ) = Σ
a_{lm}Y_{lm}(θ,φ), where
θ and φ are the → spherical polar coordinates,
Y_{lm} is the → spherical harmonic
functions, and
the sum runs over l = 1, 2, ..., ∞ and m = -l, ..., l,
where the multipole index l corresponds to angular scales
≅ 180°/l.

The quantity that gives the electric potential field due to a distribution of
charges, such as a → dipole,
→ quadrupole, → octupole, etc.
A multipole moment usually involves powers of the distance to the origin, as well as
some angular dependence.

The point in the → northern hemisphere where the
→ rotation axis of Earth touches the
→ celestial sphere. The star
→ Polaris, also called the Pole Star, is located very near this point,
at an angular separation of 42 degrees (about 1.4 lunar diameters).

1) Either extremity of the axis of the Earth or of any spherical body.
2) Either of the two regions or parts of an electric battery, magnet, or the like,
at which the magnetic flux density is concentrated.
3) → pole of a mirror.
4) The fixed point in a system of polar coordinates that serves as the origin.

M.E., from L. polus "end of an axis, the sky," from Gk. polos
"pivot, pole," polein "move around;" from PIE base *kwel-
"to turn, move around, sojourn, dwell;" cognate with Pers. carx
"every thing performing a circulatory motion; a wheel; a cart;" Av.
caxra- "wheel," caraiti "he moves, approaches;" cf.
Skt. cakra- "wheel, circle; cycle," carati "he moves, wanders;"
Gk. kyklos "circle, wheel" (loaned L.L. cyclus);
L. colere "to dwell in, to cultivate, move around," colonus
"farmer, settler;" O.E. hweol "wheel;" Rus. koleso "wheel."

Qotb, from Ar. quTb.

pole of a mirror

قطب ِ آینه

qotab-e âyene

Fr.: pôle de mirroir

The point where the → principal axis
passes through the mirror.

A star that lies in the direction pointed to by the Earth's
→ rotation axis.
The term usually refers to the star → Polaris,
which is the current → north celestial pole
star. The → south celestial pole
is not associated with any bright star.

A set of either two → electric dipoles or
two → magnetic dipoles
in close proximity to each other arranged with alternating polarities
and acting as a single unit. Quadrupole interactions are much smaller than
dipole interactions, but can allow transitions
forbidden in dipole moment transitions.

From L. quadru-, variant of quadri- "four" +
→ pole, on the model of → dipole.

A quantity characterizing an electric charge distribution,
determined by the product of the charge density, the second power of the
distance from the origin, and a spherical harmonic over the charge distribution.