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HW6_solutions

# HW6_solutions - EEE 241 Solution to Assignment#7 P.6-3 A...

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EEE 241 Solution to Assignment #7 P.6-3 A current I flows in the inner conductor of an infinitely long coaxial line and returns via the outer conductor. The radius of the inner conductor is a , and the inner and outer radii of the outer conductor are b and c , respectively. Find the magnetic flux density B for all regions and plot | B | versus r . 0.1 Solution b a c Solution: Assume current I flows in the + z -direction in the inner conductor with uniform current density given by J i = ˆ a z I πa 2 Assume current I flows in the - z -direction in the outer conductor with uniform current density given by J O = - ˆ a z I π ( c 2 - b 2 ) From symmetry and Ampere’s circuital law, we have B = ˆ a φ μ 0 I encl 2 πr 1

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Evaluation of I encl yields I encl = ( r a ) 2 I , 0 r a I , a < r < b parenleftBig c 2 r 2 c 2 b 2 parenrightBig I , b r c 0 , r > c Hence, B = ˆ a φ μ 0 Ir 2 πa 2 , 0 r a ˆ a φ μ 0 I 2 πr , a < r < b ˆ a φ μ 0 I 2
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HW6_solutions - EEE 241 Solution to Assignment#7 P.6-3 A...

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