problemset3

2 h b 2 1 2 i a2 2 ab z i 10 problem set 3 6641

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Unformatted text preview: 2 b −2 −a 2 P = origin II y a I III x IV b Figure 11: Magnetic field at centerpoint of rectangular line current (Image by MIT OpenCourseWare.) 8 Problem Set 3 6.641, Spring 2009 ⎡ ˆz ⎢ Ii → − H =− ⎣ 4π � ⎤ 4 4 ⎥ �ab �ab +� �� � � b �2 � 1 � b �2 � a � 2 � 1 ⎦ 2 2 2 a2 a + 2 b2 2 + 2 2 �2 � 2 i → −2I a + b ˆz − H= 1 πab(a2 + b2 ) 2 1 → −2I (a2 + b2 ) 2 ˆ − H= iz π ab B Figure 12: Line current in circular coil (Image by MIT OpenCourseWare.) → − I = −Iˆφ i 1 → − H= 4π � 1 4π � = 2π � � −Iˆφ × (−ˆr )adφ i i a2 0 2π 0 −ˆz Iadφ i a2 I − → H = − ˆz i 2a 9 Problem Set 3 6.641, Spring 2009 I a P Figure 13: Line current with semi-circular bump (Image by MIT OpenCourseWare.) C Contributions from left and right straight line segments are each zero because J (r� ) × ir� r = I ix × ir� r = I ix × (±ix ) = 0 1 → − H= 4π � π 0 (−Iˆφ ) × (−ˆr )adφ i i 2 a (semi-circular bump) I − → H = −...
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This document was uploaded on 03/19/2014 for the course EECS 6.641 at MIT.

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