A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is

Step-by-step solution

Consider an element of thickness dr at a distance r from the centre of spiral coil. Number of turns in coil = n Number of turns per unit length = n b - a Number of turns in element d r=d n Number of turns per unit length in element d r = ndr b - a ie, dn = ndr b - a Magnetic field at its centre due to element d r is gathered dB = ₀ Idn 2 r = ₀ I 2 n ( b - a ) dr r B = _ a ^ b ₀ Indr 2( ~b - a ) r = ₀ In 2( ~b - a ) _ a ^ b dr r = ₀ In 2( ~b - a ) _ e ( b a ) gathered