Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I₁ and COD carries a current I₂. The magnetic field on a point lying at a distance ‘d’ from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by

$fraction numerator straight mu subscript 0 over denominator 2 straight pi end fraction space open parentheses fraction numerator straight I subscript 1 plus straight I subscript 2 over denominator straight d end fraction close parentheses to the power of 1 divided by 2 end exponent$
$fraction numerator straight mu subscript 0 over denominator 2 πd end fraction space left parenthesis straight l subscript 1 superscript 2 space plus space straight I subscript 2 superscript 2 right parenthesis to the power of 1 divided by 2 end exponent$
$fraction numerator straight mu subscript 0 over denominator 2 πd end fraction left parenthesis straight I subscript 1 space plus straight I subscript 2 right parenthesis$
$fraction numerator straight mu subscript 0 over denominator 2 πd end fraction left parenthesis straight I subscript 1 superscript 2 space plus space straight I subscript 2 superscript 2 right parenthesis$

Solution

fraction numerator straight mu subscript 0 over denominator 2 πd end fraction space left parenthesis straight l subscript 1 superscript 2 space plus space straight I subscript 2 superscript 2 right parenthesis to the power of 1 divided by 2 end exponent

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