problemset1

641 spring 2009 figure 2 a diagram of a wire carrying

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Unformatted text preview: a (r3 − b3 ) ⎪ b3 ρ b ⎩ + ; 4�0 r2 3�0 r2 r < b b<r<a r<b b<r<a C Again: n · (�0 E a − �0 E b ) = σs ˆ � E (r = a+ ) = 0 ρb b3 ρa (a3 − b3 ) + ← by part (a) 4�0 a2 3�0 a2 � � � σs = ˆr · −�0 E (r = a− ) , so: i � � ρb b3 ρa (a3 − b3 ) σs = − + 4�0 a2 3�0 a2 Er (r = a− ) = D r<b Qb = π b3 ρb b < r < a Qa = 4 π (a3 − b3 )ρa 3 Qσ (r = a) = σs 4πa2 = −4πa2 Qσ = Qb + Qa + Qσ = 0 3 � ρb b3 4�0 a2 + ρa (a3 −b3 ) 3�0 a2 � Problem Set 1 6.641, Spring 2009 Figure 2: A diagram of a wire carrying a non-uniform current density and the return current at r = a (Image by MIT OpenCourseWare). Problem 1.3 A We are told current in +z direction inside cylinder r < b Current going through cylinder: � = Itotal = �a J · d� = b � S 0 2π � 0 � � J 2πb2 J0 r ˆ � 0 iz · rdφdriˆ = z b 3 � �� � � �� � � � J � |K | = Total current in sheet length...
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This document was uploaded on 03/19/2014 for the course EECS 6.641 at MIT.

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