Problem 3.337

An iron core shaped as a doughnut with round cross-section of radius \(a=3.0 \mathrm{~cm}\) carries a winding of \(N=1000\) turns through which a current \(I=1.0\) A flows. The mean radius of the doughnut is \(b=32 \mathrm{~cm} .\) Using the plot in Fig. \(3.76,\) find the magnetic energy stored up in the core. A field strength \(H\) is supposed to be the same throughout the cross-section and equal to its magnitude in the centre of the cross-section.