Question

A straight, long wire carries a current of $20A$. Another wire carrying equal current is placed parallel to it. If the force acting on a length of $10cm$ of the second wire is $2.0\times {10}^{-5}N$, what is the separation between them?

Answer 1

Force acting on $10cm$ of wire is $2\times {10}^{-5}N$

$\frac{dF}{dI}=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$

$\Rightarrow \frac{2\times {10}^{-5}}{10\times {10}^{-2}}=\frac{{\mu }_0\times 20\times 20}{2\pi d}$

$\Rightarrow d=\frac{4\pi \times {10}^{-7}\times 20\times 20\times 10\times {10}^{-2}}{2\pi \times 2\times {10}^{-5}}=400\times {10}^{-3}=0.4m=40cm$