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hw12a - aldawsari(ma28683 HW12 Betancourt(16856 This...

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aldawsari (ma28683) – HW12 – Betancourt – (16856) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 28.6-28.8 001 (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 0 i ( a 2 b 2 ) 2 π r 1 ( r 2 1 b 2 ) 2. B ( r 1 ) = μ 0 i ( a 2 r 2 1 ) 2 π r 1 ( a 2 b 2 ) 3. B ( r 1 ) = μ 0 i r 1 2 π a 2 4. B ( r 1 ) = μ 0 i r 1 2 π b 2 5. B ( r 1 ) = μ 0 i π r 1 6. B ( r 1 ) = 0 7. B ( r 1 ) = μ 0 i ( a 2 + r 2 1 2 b 2 ) 2 π r 1 ( a 2 b 2 ) 8. B ( r 1 ) = μ 0 i r 1 2 π c 2 correct 9. B ( r 1 ) = μ 0 i ( r 2 1 b 2 ) 2 π r 1 ( a 2 b 2 ) 10. B ( r 1 ) = μ 0 i 2 π r 1 Explanation: Ampere’s Law states that the line inte- gral contintegraldisplay vector B · d vector around any closed path equals μ 0 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 0 I en , where r 1 is the radius of the circle and I en is the current enclosed. For r 1 < c , B = μ 0 I en 2 π r 1 = μ 0 parenleftbigg i π r 2 1 π c 2 parenrightbigg 2 π r 1 = μ 0 i parenleftbigg r 2 1 c 2 parenrightbigg 2 π r 1 = μ 0 i r 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 0 i ( r 2 2 b 2 ) 2 π r 2 ( a 2 b 2 ) 2. B ( r 2 ) = μ 0 i ( a 2 + r 2 2 2 b 2 ) 2 π r 2 ( a 2 b 2 ) 3. B ( r 2 ) = μ 0 i r 2 2 π b 2 4. B ( r 2 ) = μ 0 i r 2 2 π a 2 5. B ( r 2 ) = μ 0 i ( a 2 b 2 ) 2 π r 2 ( r 2 2 b 2 ) 6. B ( r 2 ) = μ 0 i ( a 2 r 2 2 ) 2 π r 2 ( a 2 b 2 )

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aldawsari (ma28683) – HW12 – Betancourt – (16856) 2 7. B ( r 2 ) = μ 0 i 2 π r 2 correct 8. B ( r 2 ) = μ 0 i r 2 2 π c 2 9. B ( r 2 ) = μ 0 i π r 2 10. B ( r 2 ) = 0 Explanation: For c < r 2 < b , B = μ 0 I en 2 π r 2 = μ 0 ( i ) 2 π r 2 = μ 0 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 )?
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hw12a - aldawsari(ma28683 HW12 Betancourt(16856 This...

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