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ECE309-2008-hw8

# ECE309-2008-hw8 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 8 — Magnetization and Faraday’s Law Due: Friday, November 7 1. 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. 2. 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. 3. Suppose the magnetic flux density inside a large piece of magnetic material is ~ B 0 , so that the magnetic field is ~ H 0 = 1 μ 0 ~ B 0 - ~ M . (a) A small needle-shaped cavity is hollowed out of the material. Find the field at the center of this cavity in terms of ~ B 0 and ~ M . Also find ~ H at the center of the cavity in terms of ~ H 0 and ~ M .

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ECE309-2008-hw8 - ECE 309 Electromagnetic Fields University...

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