Question

A current of $10A$ passes through two very long wires held parallel to each other and separated by a distance of $1m$. What is the force per unit length between them?

Answer 1

Force on one wire due to other is $F=B{I}_{2}l$ where magnetic field $B=\frac{{\mu }_0{I}_1}{2\pi r}$ due to first wire at distance $r$.

Thus force per unit length between them is $F/l=B{I}_2=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}=\frac{(4\pi \times {10}^{-7})\times 10\times 10}{2\pi \times 1}=2\times {10}^{-5}N/m$