Chapter One: Vector Analysis The use of vectors and vector analysis ...
Chapter One: Vector Analysis The use of vectors and vector analysis ...
Chapter One: Vector Analysis The use of vectors and vector analysis ...
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Electromagnetic <strong>The</strong>orem<br />
(Dr. Omed Ghareb Abdullah) University <strong>of</strong> Sulaimani –College <strong>of</strong> Science – Physics Department<br />
aˆr<br />
a. (ln r)<br />
<strong>and</strong> b. <br />
2 (ln r)<br />
<br />
1<br />
2<br />
r<br />
r<br />
<br />
3 2 2<br />
Q 14 / Let G x y z aˆ<br />
, then calculate: a. G <br />
, b. G <br />
, c. G <br />
, d.<br />
G x<br />
x<br />
Q 15 / Evaluate<br />
V , V<br />
, <strong>and</strong> V<br />
if :<br />
Q 16 / If<br />
2<br />
a. V 3 x y x z , b. V z cos<br />
, c. V 4r<br />
2 cos sin<br />
.<br />
<br />
r x aˆ<br />
x<br />
y aˆ<br />
y<br />
z aˆ<br />
z<br />
<br />
is the position <strong>vector</strong> <strong>of</strong> point (x,y,z) <strong>and</strong> r r , then which <strong>of</strong><br />
<br />
r<br />
the following is incorrect: a. r , b. r 1 , c. <br />
2 ( r r<br />
) 6<br />
r<br />
, d. r 0 .<br />
Q 17 / Determine which <strong>of</strong> the following <strong>vector</strong> fields is harmonic, solenoid or conservative ;<br />
<br />
<br />
<br />
2<br />
2 2<br />
<br />
a. A 2 x y aˆ<br />
x<br />
y aˆ<br />
y<br />
, b. B x aˆ<br />
x<br />
y aˆ<br />
y<br />
2 z aˆ<br />
z<br />
, c. C ( 3 ) aˆ<br />
z aˆ<br />
z<br />
1<br />
<br />
1<br />
<br />
r<br />
d. D aˆ<br />
r<br />
, e. E r ar<br />
r<br />
e ˆ<br />
sin<br />
cos<br />
, f. F aˆ<br />
<br />
aˆ<br />
2 2 <br />
<br />
75
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