= Oscillation of a uniformly wound coil
For a light nonmagnetic rod of length $l$ wound uniformly with $N$ thin turns of mean radius $a$, the <magnetic dipole moment> is $m_B=NI\pi a^2$. Wire of cross-sectional <area> $A_w$ and <density> $\rho$ has <mass> approximately $M=2\pi aN\rho A_w$. The transverse central <moment of inertia> is $J=M(l^2/12+a^2/2)$ in the thin-winding approximation. Consequently the oscillation period in a transverse <magnetic field> does not depend on the number of turns: wire inertia and magnetic moment both scale with $N$.
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