Question
The magnetic force between wires as shown in figure is :-
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Answer
Magnetic field at $\mathrm{dr}, \mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}$
Force on small element at a distance $r$ of wire of length $L$ is $d F=i(d r)\left(\frac{\mu_{0} I}{2 \pi r}\right)$
$\mathrm{F}=\frac{\mu_{0} \mathrm{i} \mathrm{I}}{2 \pi} \int_{\mathrm{x}}^{\mathrm{x}+\mathrm{L}} \frac{\mathrm{dr}}{\mathrm{r}}=\frac{\mu_{0} \mathrm{i} \mathrm{I}}{2 \pi} \ln \left(\frac{\mathrm{x}+\mathrm{L}}{\mathrm{x}}\right)$
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