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.