Solution

For two thin conducting flat plates of width d separated by a distance" h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain$H = I/d $and$ B = \mu_0 I/d$

The magnetic flux per unit length crossing the area$h \times 1$between the plates is

$\Phi' = B h = \mu_0 I h / d$ Therefore, the inductance per unit length is:

$L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$

Substituting the numerical values
$(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$

$L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$

$\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$