HW4 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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UNIVERSITY OF CALIFORNIA Santa Barbara Department of Electrical and Computer Engineering Problem Set No. 4 Issued: October 22, 2008 Fall 2008 Due: October 29, 2008 ECE 201A Midterm: Midterm will be on November 12, 2008 between 10:00 AM- 11:50 AM in Phelps 3515. All the material covered till the end the lecture on 10/29/2008 and homework 1 - 4 will be included in the exam. The exam will be closed book. Formulas and equations too hard to remember or derive will be provided. Please bring a blue book for the exam. 1. Consider the small loop of constant current I as shown in the Figure below. Show that the magnetic vector potential is y I a x z φ θ φ r AA Ia fd y φφ π == = 0 0 2 4 cos '' where f jk r a ra ra r a = −+ +− exp( sin cos sin cos ' ' 22 2 2 θφ Expand f in a Maclaurin series about a = 0 and show that A Ia e jk r r a jkr ⎯→ ⎯+ 0 2 2 4 1 () s i n which is the vector potential of an infinitesimal loop of electric current. The quantity I a 2 = IS where S is the area of the loop is called the magnetic moment of the loop.
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HW4 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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