Chapter One: Vector Analysis The use of vectors and vector analysis ...

Electromagnetic Theorem
(Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department
Orthogonal Coordinate Systems:
The most standardd orthogonal coordinate
systems that are commonly used are:
(1) Cartesian (or Rectangular) Coordinate System , ,
(2) Spherical Coordinate System
, ,
(3) Cylindrical Coordinate System
, ,
Spherical Polar Coordinates:
The spherical plot coordinates
, , of a point are definedd in Fig;
∶ 0 ⟶ ∞
∶ 0 ⟶
∶ 0 ⟶ 2
: is the distance from the origin (the magnitude of the
position vector).
: the angle down from the z‐axis, is called
the polar angle.
: the angle around
from the x‐axis, is the azimuthal angle.
Their relation to Cartesian coordinates , , can read from the
figure.
sin cos
sin sin
cos
Any vector can be expressed as:
, & are the
radial, polar & azimuthal components of .
, & are unit vectors, pointing in the direction of
increase of
the corresponding
coordinates.
In terms of the Cartesian unit vectors:
sin
cos sin sin cos
coscos cos sin sin
sin cos