= Solution
For the closed untapered torus, apply the <magnetostatic Ampère law> to a circular path through the core. It links all $N$ turns, each carrying <electric current> $I$:
$$
\oint\mathbf H\cdot d\mathbf l=NI.
$$
Since $L\gg R$, variation of the path length and of the tangential <magnetic field intensity> across the section is negligible. Thus $H_{\rm in}L\simeq NI$, giving, within this thin-torus approximation,
$$
\boxed{H_{\rm in}=\frac{NI}{L}.}
$$
The units are $\mathrm{A\,m^{-1}}$. The core <magnetic flux density> is $B_{\rm in}=\mu_0\mu NI/L$ in the linear material model.
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