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
Q 2 / prove that:
( V A)
V
A V
A , where V is a scalar field and A is a vector
field?
Q 3 / Show that:
Q 4 / Given vectors
2
2
( A B)
( A B)
( A B
A
aˆ
x
2aˆ
y
3aˆ
z
2
) .
, B 3aˆ
x
4aˆ
y
and
C 3aˆ
y
4aˆ
z
, find the
following:
a. A and aˆ
A
, b. the component of B along C , c.
AC
, d. A
C
,
e. A ( B C)
, f. A ( B C)
, g. aˆ x
B , h. ( A
aˆ
y
). aˆ
z
.
Q 5 / Express the unit vector directed toward the point ( 0,0, h ) from an arbitrary point in the
plane z 2
. Explain the result as h 2
?
x aˆ
ˆ
x
y a
y
Ans.
( h 2) aˆ
z
2 2
2
x y ( h 2)
Q 6 / Given A 4aˆ
10aˆ
and
B 2aˆ
3aˆ
, find the magnitude and vector
y
z
y
x
components of A on B ?
Q 7 / Find the angle between A 10aˆ
2aˆ
, and B 4aˆ
0.5aˆ
, using both dot and
cross product.
Q 8 / Given A aˆ
aˆ
x
y
,
B 2aˆ
z
and
z
y
C aˆ
x
3aˆ
y
y
, find both
A B C and ( A B)
C ? Ans. 4 , 8
âz
.
Q 9 / Given A ( y 1)
aˆ
2 x aˆ
, find the vector at point ( 2,2,1)
and its projection on vector
Q 10 / If
B
, where B 5aˆ
aˆ
2aˆ
?
x
x
x
y
F F x
aˆ
, what can be said about F if ;
1. F 0 every where ,
2. F 0 every where ,
y
z
z
3. F 0 and F 0 every where?
2
3
3
Q 11 / Given field A 3 x y z aˆ
x z aˆ
( x y 2 z)
aˆ
x
y
z
, it can be said that A is :
a. Harmonic, b. Divergenceless, c. Solenoid, d. Rotational, e. Conservative.
Q 12 / If a vector field A is solenoid, which of the following is true:
a. A dl 0 , b. A ds 0 , c. A 0 , d. A 2
0 , e. A 0 .
L
S
Q 13 / If ( r
) is the position vector of point (x,y,z) and r r , then prove that :
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