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 (Dr. Omed G<br />
Department<br />
<br />
Ghareb Abdullah) University <strong>of</strong> Sulaimani –College <strong>of</strong> Science – Physics D<br />
∙ <br />
4<br />
<br />
Evidently<br />
the total flux is:<br />
∙ 160<br />
12122 420<br />
3‐ Volume integrals:<br />
A volume<br />
integral is an expression <strong>of</strong> the form:<br />
<br />
<br />
where is a scalar function <strong>and</strong> is an infinitesimal volume element:<br />
in Cartesian coordinates:<br />
<br />
Occasionally we shall encounter volume integrals <strong>of</strong> <strong>vector</strong> functions:<br />
<br />
<br />
beca<strong>use</strong> the unit <strong><strong>vector</strong>s</strong> are constants, they<br />
come outside the integral.<br />
Example:<br />
Calculate<br />
the volume<br />
integral <strong>of</strong> <br />
over the prism in Fig.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
1 <br />
2 <br />
<br />
<br />
<br />
3 3 0 2 2 <br />
3 <br />
4 1 0 9 1 12 3 8
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