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 d r 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 i.e., d n= n d r b-a Magnetic field at its centre due to element d r is d B= ₀ I d n 2 r = ₀ I 2 n (b-a) d r r B= _a^b ₀ I n d r 2(b-a) r = ₀ I n 2(b-a) _a^b d r r = ₀ I n 2(b-a) _e ( b a )