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
P
Q
E cos
aˆ
F
P Q
Q
aˆ
Q
(
P aˆ
) aˆ
2aˆ
ˆ ˆ
x
a
y
2 az
aˆ
Q
3
2 aˆ
ˆ 2 ˆ 2 ˆ ˆ 2 ˆ
x
a
y
az
ax
a
y
a
( P aˆ
) ˆ (2 ˆ ˆ
Q
aQ
a
x
az
)
3 3
4 2
2
P (2aˆ
ˆ 2 ˆ ) (2 ˆ ˆ 2 ˆ
Q
x
a
y
a
z
ax
a
y
az
)
9
9
Q
Q
z
Example(15):
Find the distance between the following pairs of points:
a‐ P 1 (1,1,2) and P 2 (0,2,2)
b‐ P 1 (2, ,1) and P2
(4, ,0)
,
3
2
c‐ P
1( 3, , ) and P2
(4, , ) .
2
2
Solution:
(a).
2
2
2
P P (1 0) (2 2) (1 2) 2
1 2
unit
(b).
x
x
p
p1
p2
1
p
cos
2 cos60 1
cos
4 cos90 0
2
1
2
1
2
(1 0)
2
(1.73 4)
2
y
(1 0)
p1
y
2
sin
2sin 60 1.73
p2
1
sin
4sin 90 4
2
1
2.06 unit
2
z
p1
z
1
p2
0
(c).
x
x
p1
p2
p p
1
r sin
cos
3sin
cos90 0
r
2
1
2
1
sin
cos
4sin 90cos
4
2
1
2
(0 ( 4))
2
(0 0)
2
( 3
0)
2
y
p1
y
r sin
sin
2sin
sin 60 0
p2
1
r
2
sin
sin
4sin 90sin
0
16 9 5 unit
1
2
1
2
z
p1
r cos
3cos
3
z
1
p2
r
2
1
cos
4cos90 0
2
Example(16):
Convert the coordinates of the following points from Cartesian to cylindrical and spherical
coordinates : a‐ P 1 (1,2,0) , b‐ P 2 (0,0,3) and c‐ P 3 (1,1,2)
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