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Q.
Two $10\, cm$ long, straight wires, each carrying a current of $5 \,A$ are kept parallel to each other. If each wire experienced a force of $10^{-5} \,N$, then separation between the wires is ___ $cm$.
It should be mentioned, $10\, cm$ wire is part of long wire.
Force experienced by unit length of wire
$=\frac{\mu_{0} I_{1} I_{2}}{2 \pi d}, I_{1}=I_{2}=5 \,A$
Force experienced by wires of length $10\, cm$
$=\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} $
$d =50 \times 10^{-3} m$
$d =50 \times 10^{-1} cm =5 \,cm$
