= Solenoid turn density
{title2=$n=N/\ell$}
The <solenoid turn density> $n$ counts turns per unit axial length in a uniformly wound <solenoid>. The total turn count $N$ is dimensionless, whereas $n$ has units $\mathrm{m^{-1}}$. A $1000$-turn coil of length $0.50\,\mathrm m$ has $n=2000\,\mathrm{m^{-1}}$; an axial interval of length $s=0.010\,\mathrm m$ then contains $ns=20$ turns. The effective circumferential <surface current density> in the closely spaced circular-turn model is $K=nI$, with units $\mathrm{A/m}$. https://web.mit.edu/8.02t/www/test/materials/StudyGuide/guide09_revised.pdf[MIT 8.02 course notes, §9.4, equations 9.4.3–9.4.4: turns per length and surface current]{ref}.
For a single-layer <helix>, the axial advance per turn is approximately $1/n$. The circular-turn model neglects this advance and the associated axial component of <electric current>, as well as the detailed <magnetic field> close to individual wires. The number of turns around the whole coil is always $N=n\ell$ here; it must not be substituted for $n$ in $B=\mu_0nI$.
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