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F07_hw09 - 3 x apart from an additive constant which is...

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Physics 505 Fall 2007 Homework Assignment #9 — Due Thursday, November 15 Textbook problems: Ch. 5: 5.19, 5.21, 5.22, 5.27 5.19 A magnetically “hard” material is in the shape of a right circular cylinder of length L and radius a . The cylinder has a permanent magnetization M 0 , uniform throughout its volume and parallel to its axis. a ) Determine the magnetic field ~ H and magnetic induction ~ B at all points on the axis of the cylinder, both inside and outside. b ) Plot the ratios ~ B/μ 0 M 0 and ~ H/M 0 on the axis as functions of z for L/a = 5. 5.21 A magnetostatic field is due entirely to a localized distribution of permanent magne- tization. a ) Show that Z ~ B · ~ H d 3 x = 0 provided the integral is taken over all space. b ) From the potential energy (5.72) of a dipole in an external field, show that for a continuous distribution of permanent magnetization the magnetostatic energy cna be written W = μ 0 2 Z ~ H · ~ H d 3 x = - μ 0 2 Z ~ M · ~ H d
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Unformatted text preview: 3 x apart from an additive constant, which is independent of the orientation or posi-tion of the various constituent magnetized bodies. 5.22 Show that in general a long, straight bar of uniform cross-sectional area A with uni-form lenghwise magnetization M , when placed with its flat end against an infinitely permeable flat surface, adheres with a force given approximately by F ’ μ 2 AM 2 Relate your discussion to the electrostatic considerations in Section 1.11. 5.27 A circuit consists of a long thin conducting shell of radius a and a parallel return wire of radius b on axis inside. If the current is assumed distributed uniformly throughout the cross section of the wire, calculate the self-inductance per unit length. What is the self-inductance if the inner conductor is a thin hollow tube?...
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