Question

Two $10cm$ long, straight wires, each carrying a current of $5A$ are kept parallel to each other. If each wire experienced a force of $10^{-5}N$, then separation between the wires is ___ $cm$.

Answer 1

Answer: 5

It should be mentioned, $10cm$ wire is part of long wire.
Force experienced by unit length of wire
$=\frac{{\mu }_0{I}_1{I}_2}{2\pi d},I_1=I_2=5A$

Force experienced by wires of length $10cm$
$=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}\times 10\times 10^{-2}$
$10^{-5}=\frac{2\times 10^{-7}\times 5\times 5}{d}\times 10\times 10^{-2}$
$d=50\times 10^{-3}m$
$d=50\times 10^{-1}cm=5cm$