ECE-305-Lecture16

ECE-305-Lecture16 - Engineering Electro-Magnetics...

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Unformatted text preview: Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 16 Dennis McCaughey, Ph.D. 23 March 2010 03/23/2010 Dennis McCaughey, ECE305, Spring 2010 2 Stokes Theorem: Stokes Theorem: ( 29 Applying the curl to one of the incremental surfaces right hand normal to the surface The subscript on indicates the path is the perimeter of an incremental area . Thus S N S S d S N d S d S H L H L H L B ( 29 ( 29 ( 29 ( 29 or Every interior wall is covered once in each direction All interior contributions will cancel Only the outside perimeter is left N N S S a d a S d d = H H L H H S H L H S B B Stokes theorem allows us to determine the point form of Amperes circuital law from its integral form and vice versa Stokes theorem equates a line integral to a surface integral ( 29 s d I d = = H L H S 03/23/2010 Dennis McCaughey, ECE305, Spring 2010 3 Example (Line Integral) Example (Line Integral) 1 2 3 2 6 sin 18 sin cos 6 sin 18 sin cos sin sin 6 sin 18 sin cos sin 6 sin 18 si r r r r r r r r d d d d H a H a H a r a r a H r H H r d dra rd a r d a d H dr H rd H r d d r dra a r r d a a r dr r = + + = + + = + = = = = + + = + + = + = + H L H L H L H L H H L H L H L ( 29 ( 29 ( 29 2 2 2 n cos 6 sin 18 sin cos paths 1 4,0 0.1 , 2 4, 0.1 ,0 0.3 3 4,0 0.1 , 0.3 r d H dl r dr H dl H dl r d r r r...
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ECE-305-Lecture16 - Engineering Electro-Magnetics...

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