A toroidal inductor has a circular cross$-$section of radius $a.$ The toroid has $N$ turns and radius $R.$ The toroid is narrow $(aR),$ so the magnetic field inside the toroid can be considered to be uniform in magnitude.

What is the self$-$inductance $L$ of the toroid?

$L=\frac{{}_0{N}^2{a}^2}{2R}$

$L=\frac{{}_0{N}^2{a}^2}{2R}$

$L=\frac{{}_0{N}^2{a}^2}{R}$

$L=\frac{{}_0{N}^{2}A}{l}$