Identify internal inductance formula

The internal self-inductance per unit length for a long cylindrical conductor is independent of its radius $r$. The formula is derived as $L_{int} = \frac{\mu_0}{8\pi}$ Henry per meter.

$L_{int} = \frac{\mu_0}{8\pi}$

Analyze the dependency on dimensions

From the formula $L_{int} = \frac{\mu_0}{8\pi}$, we observe that the term involves only the permeability of the medium $\mu_0$. There is no variable for the radius $r$ or diameter $d$ in the expression for internal inductance.

$L_{int} \neq f(r)$

Conclusion

Since internal inductance is independent of the diameter of the conductor, doubling the diameter will result in no change to the internal inductance value.

$L_{new} = L_{old} = 1 \text{ kH/m}$