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

Step-by-step solution

An element is assumed at distance x from center whose width is d x . 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