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 $\dots \; cm$.
JEE MAIN 2022, Medium
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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 $10 \; cm$
$=\frac{\mu_{0} I _{1} I _{2}}{2 \pi d } \times 10 \times 10^{-2}$
$10^{-5}=\frac{2 \times 10^{-7} \times 5 \times 5}{ d } \times 10 \times 10^{-2}$
$d =50 \times 10^{-3} \; m$
$d =50 \times 10^{-1} cm =5 \; cm$
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