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Physics-

General

Easy

Question

A and B are two concentric circular conductors of centre O and carrying current i₁ and i₂ as shown in the diagram. If ratio of their radii is 1:2 and ratio of the flux densities at O due to A and B is 1:3 then the value of $fraction numerator i subscript 1 end subscript over denominator i subscript 2 end subscript end fraction$ will be :–

$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{4}$
$\frac{1}{6}$

The correct answer is: $fraction numerator 1 over denominator 6 end fraction$

$fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction equals fraction numerator mu subscript 0 end subscript i subscript 1 end subscript over denominator 2 r end fraction cross times fraction numerator 2 left parenthesis 2 r right parenthesis over denominator mu subscript 0 end subscript i subscript 2 end subscript end fraction equals fraction numerator 1 over denominator 3 end fraction rightwards double arrow fraction numerator i subscript 1 end subscript over denominator i subscript 2 end subscript end fraction equals fraction numerator 1 over denominator 6 end fraction$

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