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Unformatted text preview: Rodriguez, Brandon – Homework 14 – Due: Oct 10 2006, 11:00 am – Inst: Andrew J Rader 1 This printout should have 8 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Please notice that for your homework to be considered towards your grade, it needs to be submitted one hour before the corresponding recitation starts. Work submitted after this time, but before the DUE DATE on top of this page, will be accepted but not graded. PLEASE REMEMBER THAT YOU MUST CARRY OUT YOUR CALCULA TIONS TO AT LEAST THREE SIGNIFI CANT FIGURES. YOUR ANSWER MUST BE WITHIN ONE PERCENT OF THE CORRECT RESULT TO BE MARKED AS CORRECT BY THE SERVER. 001 (part 1 of 4) 5 points The figure below shows a straight cylinderical 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 fl i in ⊗ F E D C r 1 r 2 r 3 r 4 c b a Which expression gives the magnitude B ( r 1 ) at F of the magnetic field in the re gion r 1 < c ? 1. B ( r 1 ) = μ i ( r 2 1 b 2 ) 2 π r 1 ( a 2 b 2 ) 2. B ( r 1 ) = μ ir 1 2 π b 2 3. B ( r 1 ) = μ i 2 π r 1 4. B ( r 1 ) = μ ir 1 2 π a 2 5. B ( r 1 ) = μ i π r 1 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 ) = μ i ( a 2 b 2 ) 2 π r 1 ( r 2 1 b 2 ) 8. B ( r 1 ) = μ i ( a 2 r 2 1 ) 2 π r 1 ( a 2 b 2 ) 9. B ( r 1 ) = μ ir 1 2 π c 2 correct 10. B ( r 1 ) = 0 Explanation: Ampere’s Law states that the line inte gral I ~ 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 is simplified to B (2 π r 1 ) = μ i in , where r 1 is the radius of the circle and i in is the current enclosed. For r 1 < c , B = μ I in 2 π r 1 = μ µ i π r 2 1 π c 2 ¶ 2 π r 1 = μ i µ r 2 1 c 2 ¶ 2 π r 1 = μ ir 1 2 π c 2 ....
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This note was uploaded on 10/18/2010 for the course PHYSICS 251 taught by Professor Pedon during the Spring '08 term at IUPUI.
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