Two identical wires A and B, each of length ‘l’, carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side ‘a’. If B_A and B_B are the values of the magnetic field at the centres of the circle and square respectively, then the ratio B_A /B_B is:

$straight pi squared over 8$
$fraction numerator straight pi squared over denominator 16 square root of 2 end fraction$

$fraction numerator straight pi squared over denominator 8 square root of 2 end fraction$

Solution

Magnetic field in case of circle of radius R, we have

$straight B subscript straight A space equals space fraction numerator straight mu subscript straight o straight I over denominator 2 straight R end fraction As comma space 2 πR space equals space straight l space left parenthesis straight l space is space length space of space straight a space wire right parenthesis straight R space equals fraction numerator straight l over denominator 2 straight pi end fraction straight B subscript straight A space equals space fraction numerator straight mu subscript straight o straight I over denominator 2 space straight x space begin display style fraction numerator straight l over denominator 2 straight pi end fraction end style end fraction space equals space fraction numerator straight mu subscript straight o Iπ over denominator straight l end fraction space... space left parenthesis straight i right parenthesis$

Magnetic field in case of square of side we get