Question

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

$fraction numerator straight mu subscript 0 straight I over denominator 2 πR end fraction$

$fraction numerator straight mu subscript 0 straight I over denominator 2 πR end fraction$
$fraction numerator straight mu subscript 0 straight I over denominator 4 πR end fraction$
$fraction numerator straight mu subscript 0 straight I over denominator straight pi squared straight R end fraction$

Solution

fraction numerator straight mu subscript 0 straight I over denominator straight pi squared straight R end fraction

straight v equals space straight I over πR dB space equals space open parentheses fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction close parentheses fraction numerator 2 straight I over denominator straight R end fraction straight I space equals space λRdθ therefore space straight B space equals space integral subscript negative straight pi divided by 2 end subscript superscript straight pi divided by 2 end superscript space dB space cos space straight theta space equals space fraction numerator straight mu subscript 0 straight lambda over denominator 2 straight pi end fraction integral subscript negative straight pi divided by 2 end subscript superscript straight pi divided by 2 end superscript space cos space θdθ space equals space fraction numerator straight mu subscript 0 straight lambda over denominator straight pi end fraction space equals space fraction numerator straight mu subscript 0 straight I over denominator straight pi squared straight R end fraction

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