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
Solution:
In general the Cartesian coordinates are related to cylindrical and spherical coordinates by
the following equations:
r
x
x
2
2
y
y
2
2
z
2
tan
1
tan
y
x
1
y
x
z z
cos
Therefore these points in cylindrical coordinates are given as follows:
1
z
r
x
(a).
P1
P1
1
x
2
P1
y
y
P1
2
P1
2
5
P1
and
tan
1
y
x
P1
P1
z
P1
0
tan
1
2
63
1
and
z
P1
0
P 1(
5,63 ,0)
x
P2
(b).
0
P2
x
2
P2
y
y
P2
2
P2
0
0
P2
and
tan
1
y
x
P2
P2
z
P2
3
tan
1
0
90
0
and
z
P2
3
P
2
(0,90
,3)
x
P3
(c).
1
P3
x
2
P3
y
P3
y
1
2
P3
2
and
P3
tan
1
z
y
x
P3
P3
P3
2
tan
1
1
45
1
and
z
P3
2
P 3(
2,45 ,2)
Also these points in spherical coordinates are given as follows:
(a).
x
r
P1
P1
1
x
2
P1
y
y
2
P1
P1
z
2
2
P1
5
and
tan
P1
1
y
x
z
P1
P1
P1
0
tan
1
2
63
1
and
P1
cos
1
0
90
5
P 1(
5,63 ,90
)
xP2
0
(b).
P2
x
2
P2
y
y
P2
2
P2
0
z
2
P2
3
and
P2
z
tan
P2
1
3
y
x
P2
P2
tan
1
0
90
0
and
P2
cos
1
3
0
3
P
2
(3,90
,0
)
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