Determine the self inductance per unit length of a long solenoid with radius R and n turns per unit length.

1
\( \boxed{\mathcal{L} = \mu_0 n \pi R^2}\)
2
\( \boxed{\mathcal{L} = \mu_0 n^2 \pi R^2}\)
3
\( \boxed{\mathcal{L} = \mu_0 n^2 \pi R}\)
4
\( \boxed{\mathcal{L} = \mu_0 n \pi R}\)

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