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Unformatted text preview: Physics 505 Fall 2007 Homework Assignment #7 — Due Thursday, November 1 Textbook problems: Ch. 5: 5.4, 5.7, 5.8, 5.9 5.4 A magnetic induction ~ B in a current-free region in a uniform medium is cylindrically symmetric with components B z ( ρ,z ) and B ρ ( ρ,z ) and with a known B z (0 ,z ) on the axis of symmetry. The magnitude of the axial field varies slowly in z . a ) Show that near the axis the axial and radial components of magnetic induction are approximately B z ( ρ,z ) ≈ B z (0 ,z )- ρ 2 4 ∂ 2 B z (0 ,z ) ∂z 2 + ··· B ρ ( ρ,z ) ≈ - ρ 2 ∂B z (0 ,z ) ∂z + ρ 3 16 ∂ 3 B z (0 ,z ) ∂z 3 + ··· b ) What are the magnitudes of the neglected terms, or equivalently what is the criterion defining “near” the axis? 5.7 A compact circular coil of radius a , carrying a current I (perhaps N turns, each with current I/N ), lies in the x- y plane with its center at the origin....
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