A toroid is wound on a non-magnetic ring whose cross-section is a rectangle, as in the figure. The inner radius of the ring is $5.0\ \text{cm}$, its outer radius is $15\ \text{cm}$, and its height is $2.0\ \text{cm}$. It has $500$ turns, wound closely and evenly all round, and carries a current of $2.0\ \text{A}$. The ring is wide, so the field inside it is far from uniform across the rectangle. Take $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. What is the magnetic flux through the rectangle of one turn?

Fig. 1: A toroid with a rectangular cross-section. On the left, a top view shows the ring with closely spaced turns all round it. On the right, a cut through the axis shows the two rectangles of the cross-section, each between an inner radius of 5.0 cm and an outer radius of 15 cm from the axis, and 2.0 cm high. A note gives 500 turns and a current of 2.0 A.