Question

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 passes through the coil, the magnetic flux density at the centre is

(a) μ₀NI/b

(b) 2μ₀NI/a

(c) μ₀NI/2(b - a) In b/a

(d) μ₀I^N/2(b - a) In b/a

Answer 1

Correct Answer is: (c) μ₀NI/2(b - a) In b/a

The number of turns per unit length is N/b - a

Consider an elemental ring of radius x and width dx.

The number of turns in the ring is dN = N dx/ b - a.

The magnetic field at the centre due to the ring is dB 

∴ the field at the centre is