Two concentric coplanar circular loops of radii ' r₁ ' and ' r₂ '… | MHT CET 2021 (22 Sep, Shift 1)

Q79MHT CET 2021 · 22 SEP · SHIFT 1Medium

Biot-Savart Law & Circular Coils

Two concentric coplanar circular loops of radii ' $r_1$ ' and ' $r_2$ ' respectively carry currents ' $i_1$ ' and ' $i_2$ ' in opposite directions (one clockwise and other anticlockwise). The magnetic induction at the centre of the loops is half that due to ' $i_1$ ' alone at the centre. If $r_2 = 2r_1$ , the value of $\frac{i_2}{i_1}$

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Answer: (b)

Opposite currents: $B = \dfrac{\mu_0 i_1}{2r_1}-\dfrac{\mu_0 i_2}{2r_2} = \dfrac{1}{2}\cdot\dfrac{\mu_0 i_1}{2r_1}$
$\dfrac{i_2}{r_2} = \dfrac{i_1}{2r_1}$ ; with $r_2 = 2r_1$ : $\dfrac{i_2}{2r_1} = \dfrac{i_1}{2r_1}$
$\dfrac{i_2}{i_1} = 1$
So the answer is (b) 1.

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Biot-Savart Law & Circular Coils question from MHT CET 2021 (22 Sep, Shift 1)

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