A semi-infinite solenoid (conce ntric with the negative z-axis) has cross sectional area A = R 2

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A semi-infinite solenoid (conce ntric with the negative z-axis) has cross sectional area A = πR2, n turns per unit length of a wire with current I , and magnetic moment per unit length m = nIA. When A → 0 and N →∞ with m fixed, Application 11.1 showed that the agnetic field outside this solenoid (i.e., excluding the negative z-axis) is

Use the field inside an infinite solenoid to approximate the field Bin inside a semi-infinite, finite-area solenoid.
Show that when A → 0, Bin is confined to the negative z-axis and ∇ · Bin = −μ0mδ(r). This guarantees that ∇ · (Bin + Bout) = 0 as it must. 

Show that lim

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