A small segment of length ‘a’ is cut along z-axis from an infinite, thin sheet carrying current of linear density $j$. The magnetic field vector at ‘P’ due to the remaining part is  $\frac{{\mu }_{0}j}{N}\left(\frac{a}{\pi h}-1\right)\hat{i}$,  then $N$ is

 

$\overrightarrow{B_P}=\overrightarrow{B_1}-\overrightarrow{B_2}$, where $\overrightarrow{B_1}, \overrightarrow{B_2}$ are magnetic fields at P due to the infinite sheet (without hole) and that due to the hole alone (assumed current-carrying)

$\overrightarrow{B_1}=\frac{{\mu }_{0}j}{2}\left(-\hat{i}\right)$            (due to infinite sheet)

$\overrightarrow{B_2}=\frac{{\mu }_{0}ja}{2\mathrm{\pi h}}\left(-\hat{i}\right)$         (due to infinite long wire)

$\overrightarrow{B_P}=\frac{{\mu }_{0}j}{2}\left(-\widehat{i}\right)-\frac{{\mu }_{0}ja}{2\pi h}\left(-\widehat{i}\right)$

$\overrightarrow{B_P}=\frac{{\mu }_{0}j}{2}\left[\frac{a}{\pi h}-1\right]\hat{i}$

$\therefore$Hence $N=2$