Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are d and (d/2) for coil Y and X respectively. The radii of coils Y and X are (2r) and (r) respectively. The magnetic induction due to the bigger coil at point 'O' is By and that due to smaller coil X at point 'O' is Bx. ( d r) The relation between Bx and By is (a) By = Bx (b) By = 2Bx (c) Bx = 2By (d) Bx = 4By

Answer: (c). On the axis B = μ₀ I r²2(r²+x²)3/2 ≈ (μ₀ I r²)/(2x³) for x r. Coil X: Bx = (μ₀ I r²)/(2(d/2)³) = (4μ₀ I r²)/(d³) Coil Y: By = (μ₀ I (2r)²)/(2d³) = (2μ₀ I r²)/(d³) So Bx = 2By, answer (c).

Two circular coils X (smaller) and Y (bigger), each having a single… | MHT CET 2026 (19 Apr, Shift 1)

Q18MHT CET 2026 · 19 APR · SHIFT 1Difficult

Biot-Savart Law & Circular Coils

Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are $d$ and $\left(\frac{d}{2}\right)$ for coil Y and X respectively. The radii of coils Y and X are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point 'O' is $B_y$ and that due to smaller coil X at point 'O' is $B_x$ . ( $d \gg r$ ) The relation between $B_x$ and $B_y$ is

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Answer: (c)

On the axis $B = \dfrac{\mu_0 I r^2}{2(r^2+x^2)^{3/2}} \approx \dfrac{\mu_0 I r^2}{2x^3}$ for $x \gg r$ .
Coil X: $B_x = \dfrac{\mu_0 I r^2}{2(d/2)^3} = \dfrac{4\mu_0 I r^2}{d^3}$
Coil Y: $B_y = \dfrac{\mu_0 I (2r)^2}{2d^3} = \dfrac{2\mu_0 I r^2}{d^3}$
So $B_x = 2B_y$ , answer (c).

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Biot-Savart Law & Circular Coils question from MHT CET 2026 (19 Apr, Shift 1)

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