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HW7_solutions

# HW7_solutions - SOLUTIONS TO ASSIGNMENT 7 P.6-17 The...

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SOLUTIONS TO ASSIGNMENT 7 P.6-17 The magnetic flux density B for an infinitely long cylindrical conductor has been found in Example 6-1. Determine the vector magnetic potential A both inside and outside the conductor from the relation B A =∇× From Example 6-1, 1 2 2 o Ir B a for r b b φ μ π = r r (1) 2 2 o I B a for r b r φ μ π = r r (2) r z z A A A B A B a a z r r φ φ = ∇× = = − r r r r r (3) (since, from symmetry does not vary along ) A z r From (1) and (3), 2 1 1 2 0 4 o z Ir A a c for r b b μ π = + r r From (2) and (3) 2 2 ln 2 o z I A a r c for r b μ π = + r r The two constants of integration are related. ( ) 1 2 2 1 At , 2ln 1 4 o I r b A A C b C μ π = = = + r r 2 2 1 ln 1 4 o z I r A a c for r b b μ π = + + r r P.6-26

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HW7_solutions - SOLUTIONS TO ASSIGNMENT 7 P.6-17 The...

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