A toroid has a major radius $R$ and a minor radius $r$ and is tightly wound with $N$ turns of wire on a hollow cardboard torus. Figure $P 32.12$ shows half of this toroid, allowing us to see its cross section. If $R >> r$, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius $R$. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately