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 />
<br />
<br />
/<br />
3 2 5 cos sin <br />
<br />
<br />
sin <br />
10 <br />
3 2 <br />
/<br />
<br />
5<br />
3 <br />
We have two surfaces:<br />
1) <strong>The</strong> hemisphere:<br />
sin<br />
<br />
; : 0 → 2 ;<br />
: 0 → /2<br />
V ∙ cos sin<br />
<br />
/<br />
<br />
sincos<br />
<br />
<br />
<br />
π <br />
2) <strong>The</strong> flat bottom: sin<br />
<br />
/2 ; : 0 → 2 ; : 0 → <br />
V ∙ sin sin<br />
<br />
<br />
<br />
<br />
<br />
<strong>The</strong> total:<br />
<br />
2π <br />
3<br />
V ∙ π <br />
2π <br />
3 5 3 π <br />
Problem:<br />
Test the Gradient theorem for the function:<br />
cos sincos<br />
Using the<br />
path shown in Figure, from 0 , 0 , 0 to 0 , 0 , 2.
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