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 />
Example:<br />
Calculate the volume integral <strong>of</strong> over the volume in Fig.<br />
z<br />
(0,0,1)<br />
<br />
y<br />
(0,2,0)<br />
x<br />
(3,0,0)<br />
<br />
3 2 <br />
3 <br />
<br />
3 2 0 <br />
3 0 1<br />
20 03 06 <br />
2 3 6 <br />
Using equation <strong>of</strong> normal on the surface , <strong>and</strong> the point 3 , 0 , 0<br />
the surface equation can be found from the equation:<br />
0<br />
∴ 2 3 3 0 6 0 0<br />
2 3 6 6 0<br />
⟹ 3 3 <br />
To find the relation between <strong>and</strong> ; we <strong>use</strong> the two points<br />
<br />
<br />
<br />
<br />
⟹<br />
, ⟹ 2 , 0<br />
, ⟹ 0 , 1<br />
2<br />
0 02<br />
10<br />
⟹<br />
2 2 ⟹ 2 2 <br />
2<br />
<br />
2<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
2 <br />
<br />
<br />
<br />
25
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