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
E
F
E cos
aˆ
F
E F
F
( E aˆ
) aˆ
4 aˆ
ˆ ˆ ˆ ˆ ˆ
x
10
a
y
5 a
z
4 a
x
10
a
y
5 a
z
aˆ
F
16 100 25
141
4 aˆ
10 ˆ 5 ˆ
x
a
y
a
z
( E aˆ
) aˆ
(3aˆ
4 ˆ
F F
x
a
z
)
141
(12 20)
E (4 aˆ
10 ˆ 5 ˆ
F
x
a
y
a
z
)
141
aˆ
F
F
F
4 aˆ
x
10
aˆ
y
141
5 aˆ
z
The scalar component of E along F is given by:
E F
E
ˆ
F
E cos
E aF
F
4 aˆ
10
ˆ 5 ˆ
x
a
y
az
12 20
E aˆ
(3aˆ
4 ˆ
F
E
F
x
a
z
)
141 141
Example(14):
Three field quantities are given by: P aˆ
aˆ
,
Q 2aˆ
aˆ
2aˆ
,
2
x z
x y z
R 2aˆ
3aˆ
aˆ
,
x
y
z
determine the following:
(a). ( P Q)
( P Q)
P ( P Q)
Q
( P Q)
,
(b). Q ( R P)
(c). sin QR
(d). P ( Q R)
(e). A unit vector perpendicular to both Q and R
(f). The scalar and vector component of P along
Q
Solution:
( P Q)
( P Q)
P ( P Q)
Q
( P Q)
P P P Q Q
P Q
Q
0
Q P Q
P 0
2 P Q sinQP
(a). P 4 1
5 Q 4 1
4 3
1
Q P 4 2 2
QP
cos
72.65
P Q 3
5 3 5
sin 72.65 0.95
64