A packed bundle of $100$ long straight insulated wires forms a cylinder of radius $R = 0.5 cm$. If each wire carries a current of $2A$, then magnetic force per unit length on a wire located at $2 mm$ from the centre of the bundle is $704 \times N \times {10}^{-6}N$. Find the value of $N$.

Magnetic field at a distance of 2 mm from the centre is 

From Ampere's Law

$\int B.dl=\mu i$

Here current enclosed is 

(Excluding the wire on which force is being calculated)

$i=\frac{99\times \pi r^2}{\pi R^2}\times 2 A=31.68 A$

$\Rightarrow B=\frac{\mu i}{2\pi r}=\frac{\mu }{\pi r}\times 15.84$

Magnetic force is given by 

$F=qvB=Bil$

$\frac{F}{l}=Bi$

$=\frac{\left(15.84\right)\mu i}{\pi r}=6336\times {10}^{-6}N/m$

therefore $N=\frac{6336}{704}=9$