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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.

Asked in JEE Main 31st Aug 1st Shift 2021 · Rotating charges and multiple loops

• (1) (μ₀ I)/8[(a+b)/(a-b)]
• (2) (μ₀ I)/(4(a-b))[1/a-1/b]
• (3) (μ₀ I)/8((a-b)/(a+b))
• (4) (μ₀ I N)/(2(b-a))logₑ(b/a)

Step-by-step solution

Why the other options are wrong

• (1) Averages radii instead of integrating, and loses N
• (2) Integrates 1/(r²) instead of 1/r and loses N
• (3) Averages radii and inverts the ratio, losing N

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