Question: A magnetic induction ? in a current-free region in a uniform medium is cylindrically symmetric with components B z (?, z) and B ? (?,

A magnetic induction ? in a current-free region in a uniform medium is cylindrically symmetric with components B_z(?, z) and B_?(?, 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) What are the magnitudes of the neglected terms, or equivalently what is the criterion defining "near" the axis?

.(0, ) 2? .(, ) ~ .(0, ) - ( .(0, 2) d'B.(0, z) 2 - - (2 )' z 16

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