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I have read from my reference that the self inductance of a wire ring is derived in a non-trivial manner. I have copied an image off the result below, let me know if I should translate it to Latex.

enter image description here

My question is one regarding units. It seems the author goes straight from $\frac{s^2}{cm} to $ $H$. How can this be done? Henrys are in SI base units $\frac{kg\cdot m^2}{s^2\cdot A^2}$.

Furthermore, I have also read about the permeability of free space, $u_0$. Does that come into play here?

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