A circular loop carrying current I lies in the yz plane with its axis along the x axis.

(a) Evaluate the line integral ∫C B • dℓ along the axis of the loop from x = – ℓ1 to x = +ℓ1.

(b) Show that when ℓ1 → ∞, the line integral approaches μ0I. This result can be related to Ampere's law by closing the curve of integration with a semicircle of radius ℓ on which B ≈ 0 for ℓ very large.