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Question

A square frame of side l m carries a current I, it produces a magnetic field B1 at its centre. Same current is passed through a circular coil having the same perimeter as the square. Magnetic field at the centre of circular coil is B2. Then, the ratio B1B2 is

A
223π
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B
82π
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C
537π
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D
1
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Solution

The correct option is A 82π
For circle
I=2πR
R=l2π
For square l=4a,a=l4
Magnetic field at the centre of circular coil
B2=μ0i2R=μ0i2l2π=μ0πil
Magnetic field at the cnetre of square from.
B2=4[μ04πia(sin45o+sin45o)]
=22μoiπa=82μoiπl
B1B2=82π

740958_681156_ans_7ea0c836ff61413995d05af39efaf2fc.JPG

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