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ECE3209-2009-hw9

# ECE3209-2009-hw9 - 4 A long circular cylinder of radius R...

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ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 9 — the Magnetic Vector Potential and Magnetization Due: Friday, November 13 1. Cheng P. 6-19. For a small rectangular loop with sides a and b that carries current I , (a) Find the vector magnetic potential ~ A at a distant point P ( x,y,z ) (b) Determine the magnetic ﬂux density ~ B from ~ A . 2. Find the vector potential, ~ A , and corresponding B -ﬁeld for two inﬁnitely-long (in the z - direction) parallel currents (a transmission line) at point P = ( x,y, 0) , as shown below: 3. An inﬁnitely long circular cylinder carries a uniform magnetization of ~ M parallel to its axis. Find the bound current densities and magnetic ﬁeld due to ~ M inside and outside the cylinder.

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Unformatted text preview: 4. A long circular cylinder, of radius R , carries a magnetization ~ M = kr 2 ˆ φ , where k is a constant, r is the radial distance from the axis, and ˆ φ is the “circumferential” unit vector. Find the bound current densities and magnetic ﬁeld due to ~ M for points inside and outside the cylinder. 5. A current I ﬂows down a long straight wire of radius R . If the wire is made of linear material with magnetic susceptibility χ m , and the current is distributed uniformly, (a) what is ~ B a distance r from the center? (b) Find all the bound currents on or in the wire. What is the net bound current ﬂowing down the wire?...
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ECE3209-2009-hw9 - 4 A long circular cylinder of radius R...

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