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Electro Magnetic Theory (Coordinate System)
1. ELECTRO MAGNETIC THEORY
Coordinate System
(Cartesian, Cylindrical, Spherical)
Ms. J. Glory Priyadharshini,
Assistant Professor/EEE,
Sri Ramakrishna Institute of Technology,
Coimbatore.
2. RELATIONSHIP BETWEEN THE VARIABLES OF THE COORDINATE SYSTEMS
CARTESIAN COORDINATE SYSTEM CYLINDRICAL COORDINATE SYSTEM SPHERICAL COORDINATE SYSTEM
x 2
2
y
x
2
2
2
z
y
x
r
y
x
y
1
tan
z
y
x 2
2
1
tan
z z
x
y
1
tan
cos
x 2
2
z
r
sin
y
z
1
tan
z
z z
cos
sin
r
x
sin
r
r
sin
sin
r
y
cos
r
z
cos
r
z
RELATIONSHIP BETWEEN THE COMPONENTS OF THE COORDINATE SYSTEMS
CARTESIAN COORDINATE SYSTEM CYLINDRICAL COORDINATE SYSTEM SPHERICAL COORDINATE SYSTEM
x
A
z
y
x
z A
A
A
A
A
A
1
0
0
0
cos
sin
0
sin
cos
z
y
x
r
A
A
A
A
A
A
0
cos
sin
sin
sin
cos
cos
cos
cos
sin
sin
cos
sin
y
A
z
A
z
z
y
x
A
A
A
A
A
A
1
0
0
0
cos
sin
0
sin
cos
A
z
r
A
A
A
A
A
A
0
1
0
sin
0
cos
cos
0
sin
A
z
A
0
sin
cos
cos
sin
cos
sin
sin
sin
cos
cos
cos
sin
z
y
x
A
A
A
A
A
A
A
A
A r
z 0
sin
cos
1
0
0
0
cos
sin r
A
A
A
3. GRADIENT, DIVERGENCE AND CURL – COORDINATE SYSTEMS
GENERAL
FORMAT
GRADIENT DIVERGENCE CURL
3
3
3
2
2
2
1
1
1
1
1
1
c
c
c a
c
F
m
a
c
F
m
a
c
F
m
F
)
(
)
(
)
(
1
. 2
1
3
3
3
1
2
2
3
2
1
1
3
2
1
m
m
F
c
m
m
F
c
m
m
F
c
m
m
m
F c
c
c
3
3
2
2
1
1
3
2
1
3
3
2
2
1
1
3
2
1
1
m
F
m
F
m
F
c
c
c
a
m
a
m
a
m
m
m
m
XF
C
C
C
c
c
c
CARTESIAN
COORDINATE
SYSTEM
z
y
x a
z
F
a
y
F
a
x
F
F
z
F
y
F
x
F
F z
y
x
z
y
x
z
y
x
F
F
F
z
y
x
a
a
a
XF
CYLINDRICAL
COORDINATE
SYSTEM
z
a
z
F
a
F
a
F
F
1
)
(
)
(
)
(
1
.
z
F
z
F
F
F
z
z
F
F
F
z
a
a
a
XF
1
SPHERICAL
COORDINATE
SYSTEM
a
F
r
a
F
r
a
r
F
F r
sin
1
1
)
(
)
sin
(
)
sin
(
sin
1
. 2
2
r
F
r
F
r
F
r
r
F r
sin
sin
sin
1
2
r
F
r
F
F
r
a
r
a
r
a
r
XF
r
r
CARTESIAN COORDINATE
SYSTEM
CYLINDRICAL COORDINATE
SYSTEM
SPHERICAL COORDINATE
SYSTEM
c1,c2,c3 are coordinate
variables
x
c
1 y
c
2 z
c
3
1
c
2
c z
c
3 r
c
1
2
c
3
c
m1,m2,m3 are Scale
factors
1
1
1
dc
dl
m
2
2
2
dc
dl
m
3
3
3
dc
dl
m
iables
coordinate
the
to
ing
correspond
length
al
differenti
the
are
dl
and
dl
dl var
, 3
2
1
dx
dl
1 dy
dl
2 dz
dl
3
d
dl
1
d
dl
2 dz
dl
3 dr
dl
1
rd
dl
2
d
r
dl sin
3
1
1
dx
dx
m 1
2
dy
dy
m 1
3
dz
dz
m 1
1
d
d
m
d
d
m2 1
3
dz
dz
m 1
1
dr
dr
m r
d
rd
m
2
sin
sin
3 r
d
d
r
m