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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Recall the formula of the magnitude of the magnetic field in terms of current and permeability in free space, $B = \int_{a}^{b} \frac{μ_{0} d N i}{2 x} = \int_{a}^{b} \frac{μ_{0} (\frac{N}{b - a} d x) i}{2 x} = \frac{μ_{0} N i}{2 (b - a)} l n (\frac{b}{a})$ .

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