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JEE Main 2021 (31 Aug, Shift 1) · Biot-Savart Law & Circular Coils

Biot-Savart Law & Circular Coils question from JEE Main 2021 (31 Aug, Shift 1)

Q80JEE Main 2021 · 31 AUG · SHIFT 1Difficult

Biot-Savart Law & Circular Coils

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

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Answer: (a)

Turns per unit radial width: $\dfrac{N}{b-a}$ ; $dB = \dfrac{\mu_0 I}{2r}\cdot\dfrac{N\,dr}{b-a}$ .
$B = \dfrac{\mu_0 IN}{2(b-a)}\displaystyle\int_a^b\dfrac{dr}{r} = \dfrac{\mu_0 IN}{2(b-a)}\ln\dfrac{b}{a}$
So the answer is (a).

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