A circular iron ring with inner and outer radii of 30 cm and 40 cm has a rectangular cross section with width of 10 cm. A uniformly wound toroidal winding of 150 turns carries a current of 2 A. Let the relative permeability of iron be 500. Starting from Amp`ere's law in terms of H~ , derive the minimum and maximum magnetic field intensities in the ring. Find the corresponding magnetic flux densities. Find the magnetic flux in the ring.

In this question once we get to calculating the magnetic flux, we have the equation = Integral[z, 0] Integral[max, min] (*N*I*(a_ ))/(2**) (a_ dz d). Why do we do (a_ dz d) instead of ( dz d)