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 af o r r b b φ μ π =≤ r r (1) 2 2 o I B o r r b r =≥ r r (2) rz z AA A BA B a a zr r φφ ∂∂ ⎛⎞ ⇒ = =− ⎜⎟ ⎝⎠ r rr (3) (since, from symmetry does not vary along ) Az r From (1) and (3), 2 11 2 0 4 o z Ir Aa c f o r rb b ⎡⎤ + ⎢⎥ ⎣⎦ r r From (2) and (3) 22 ln 2 o z I r c f o r r b + r r The two constants of integration are related. () 12 2 1 At , 2ln 1 4 o I rbA A C b C == = + 2 21 ln 1 4 o z I r cf o r r b b + + r r P.6-26 A ferromagnetic sphere of radius b is magnetized uniformly with a magnetization zo M aM = r r . (a) Determine the equivalent magnetization current densities mm s J and J r r (b) Determine the magnetic flux density at the center of the sphere.
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This note was uploaded on 10/15/2008 for the course EEE 241 taught by Professor Ayanar during the Spring '07 term at ASU.

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

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