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 />
aˆ<br />
<br />
aˆ<br />
<br />
1 <br />
B <br />
<br />
<br />
0 0<br />
1<br />
B <br />
2<br />
<br />
<br />
cos<br />
aˆ<br />
<br />
aˆ<br />
z<br />
<br />
<br />
z<br />
cos<br />
<br />
sin<br />
aˆ<br />
<br />
<br />
1 <br />
aˆ<br />
<br />
<br />
<br />
<br />
sin<br />
( 0) aˆ<br />
<br />
<br />
cos<br />
(0 ) aˆ<br />
2<br />
<br />
z<br />
<br />
(0 0) <br />
<br />
Hence,<br />
<br />
s<br />
<br />
s<br />
<br />
s<br />
1<br />
( B)<br />
ds cos<br />
aˆ<br />
2<br />
s<br />
<br />
1<br />
( B)<br />
ds (cos)<br />
<br />
3 1<br />
( B)<br />
ds (0 ) <br />
2 2<br />
<br />
<br />
<br />
sin<br />
aˆ<br />
<br />
s<br />
<br />
<br />
dz d<br />
aˆ<br />
<br />
/ 2 3<br />
/ 3 0<br />
sin<br />
dz d<br />
2<br />
<br />
/ 2 3<br />
1<br />
( z)<br />
(cos<br />
/ 2 cos<br />
/ 3) (3 0)<br />
/ 3<br />
0 2<br />
3<br />
( B)<br />
ds <br />
4<br />
It is clearly seen that the left <strong>and</strong> right h<strong>and</strong> side has the same value, which indicates the<br />
validity <strong>of</strong> the Stokes’s theorem.<br />
<br />
<br />
Example (6):<br />
<br />
transform into spherical coordinate <strong>and</strong> find its magnitude at point 3, 4, 0.<br />
Solution:<br />
∙ ∙ ∙ ∙ <br />
∙ ∙ ∙ ∙ <br />
∙ ∙ ∙ ∙ <br />
<br />
∙ ∙ ∙ <br />
∙ ∙ ∙ <br />
∙ ∙ ∙ <br />
<br />
0 <br />
0 <br />
<br />
0 1 0 <br />
<br />
<br />
<br />
<br />
59
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