HW06-solutions-1 - gilbert(amg3448 – HW06 – tsoi...

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Unformatted text preview: gilbert (amg3448) – HW06 – tsoi – (57210) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 4) 10.0 points The figure below shows a straight cylindrical coaxial cable of radii a , b , and c in which equal, uniformly distributed, but antiparallel currents i exist in the two conductors. O i out i in ⊗ F E D C r 1 r 2 r 3 r 4 c b a Which expression gives the magnitude of the magnetic field in the region r 1 < c (at F )? 1. B ( r 1 ) = μ i π r 1 2. B ( r 1 ) = μ i ( a 2- b 2 ) 2 π r 1 ( r 2 1- b 2 ) 3. B ( r 1 ) = μ ir 1 2 π b 2 4. B ( r 1 ) = μ ir 1 2 π a 2 5. B ( r 1 ) = μ ir 1 2 π c 2 correct 6. B ( r 1 ) = μ i ( a 2 + r 2 1- 2 b 2 ) 2 π r 1 ( a 2- b 2 ) 7. B ( r 1 ) = 0 8. B ( r 1 ) = μ i ( r 2 1- b 2 ) 2 π r 1 ( a 2- b 2 ) 9. B ( r 1 ) = μ i ( a 2- r 2 1 ) 2 π r 1 ( a 2- b 2 ) 10. B ( r 1 ) = μ i 2 π r 1 Explanation: Ampere’s Law states that the line inte- gral , B · d , + around any closed path equals μ I , where I is the total steady current pass- ing through any surface bounded by the closed path. Considering the symmetry of this problem, we choose a circular path, so Ampere’s Law simplifies to B (2 π r 1 ) = μ I en , where r 1 is the radius of the circle and I en is the current enclosed. For r 1 < c , B = μ I en 2 π r 1 = μ i π r 2 1 π c 2 2 π r 1 = μ i r 2 1 c 2 2 π r 1 = μ ir 1 2 π c 2 . 002 (part 2 of 4) 10.0 points Which expression gives the magnitude of the magnetic field in the region c < r 2 < b (at E )? 1. B ( r 2 ) = μ i ( a 2- r 2 2 ) 2 π r 2 ( a 2- b 2 ) 2. B ( r 2 ) = 0 3. B ( r 2 ) = μ ir 2 2 π b 2 4. B ( r 2 ) = μ i ( a 2 + r 2 2- 2 b 2 ) 2 π r 2 ( a 2- b 2 ) 5. B ( r 2 ) = μ i 2 π r 2 correct 6. B ( r 2 ) = μ i ( r 2 2- b 2 ) 2 π r 2 ( a 2- b 2 ) 7. B ( r 2 ) = μ ir 2 2 π c 2 gilbert (amg3448) – HW06 – tsoi – (57210) 2 8. B ( r 2 ) = μ i ( a 2- b 2 ) 2 π r 2 ( r 2 2- b 2 ) 9. B ( r 2 ) = μ i π r 2 10. B ( r 2 ) = μ ir 2 2 π a 2 Explanation: For c < r 2 < b , B = μ I en 2 π r 2 = μ ( i ) 2 π r 2 = μ i 2 π r 2 . 003 (part 3 of 4) 10.0 points Which expression gives the magnitude of the magnetic field in the region b < r 3 < a (at D )? 1. B ( r 3 ) = μ ir 3 2 π b 2 2. B ( r 3 ) = μ i ( r 2 3- b 2 ) 2 π r 3 ( a 2- b 2 ) 3. B ( r 3 ) = μ i ( a 2- r 2 3 ) 2 π r 3 ( a 2- b 2 ) correct 4. B ( r 3 ) = μ i ( a 2- b 2 ) 2 π r 3 ( r 2 3- b 2 ) 5. B ( r 3 ) = μ i ( a 2 + r 2 3- 2 b 2 ) 2 π r 3 ( a 2- b 2 ) 6. B ( r 3 ) = μ i 2 π r 3 7. B ( r 3 ) = 0 8. B ( r 3 ) = μ ir 3 2 π a 2 9. B ( r 3 ) = μ i π r 3 10. B ( r 3 ) = μ ir 3 2 π c 2 Explanation: For b < r 3 < a , B = μ I en 2 π r 3 = μ i- i π ( r 2 3- b 2 ) π ( a 2- b 2 ) 2 π r 3 = μ i a 2- r 2 3 a 2- b 2 2 π r 3 = μ i ( a 2- r 2 3 ) 2 π r 3 ( a 2- b 2 ) ....
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HW06-solutions-1 - gilbert(amg3448 – HW06 – tsoi...

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