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

Question

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is, μ 0 N I b, 2 μ 0 N I a, μ 0 N I 2 b - a log ⁡ b a, μ 0 I N 2 b - a log ⁡ a b

MARKS App · Accepted Answer

An element is assumed at distance x from center whose width is dx. No. of turns in width b – a = N ∴ No. of turns is width d x = n = N b - a d x d B = μ 0 n i 2 x = μ 0 i N 2 b - a d x x ∴ B = μ 0 i n 2 b - a ∫ a b d x x = μ 0 N i 2 b - a log e ⁡ b a

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