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 pass through the coil, the magnetic field at the centre is
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Consider an element of thickness dr at a distance r from the centre.
The number of turns in this element is dN=N(b−a)dr
Magnetic field at the centre of the coil due to this element is dB=μ0(dn)i2r
Integrating from a to b gives the desired answer
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