A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R . The magnitude of the magnetic induction along its axis is

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d B = 2 π R μ 0 ​ di ​ [ − cos θ i ^ − sin θ j ^ ​ ] di = π R T ​ Rd θ = π I ​ d θ d B = 2 π 2 R μ 0 ​ I ​ ( − cos θ i ^ − sin θ j ^ ​ ) B = − π 2 R μ 0 ​ I ​ j ^ ​

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