Find the inductane of a unit length of a double line if the radius of each wire is `eta` times less than the distance between the axes of the wires. The field inside the wires is to be neglected, the permeability is assumed to be equal to unity throughout, and `eta gt gt 1`.

Explanation

For a single carrying wire, `B_(varphi) = (mu_(0) I)/(2pi r) (r gt a)`. For the double line cablem with current flowing in opposite directions, in the two conductors,
`B_(varphi) = (mu_(0) I)/(pi r)`, between the cables, by superposition. The associated flux is,
`Phi = int_(a)^(d -a) (mu_(0) I)/(pi) (dx xx 1)/(r) = (mu_(0)I)/(pi)` In `(d)/(a) = (mu_(0))/(pi)` In `eta xx 1`, per unit lenght
Hence, `L_(1) = (mu_(0))/(pi) In eta`
is the inductance per unit length.