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Two long straight parallel conductors are carrying currents $i_1$ and $i_2$ in the same direction. Work done per unit length, when the distance between them is doubled is
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The correct answer is:
$\frac{\mu_0}{2 \pi} i_1 i_2 \ln [2]$
$\begin{aligned} \text { Work done } & =\int_d^{2 d} F \cdot d x=\int_d^{2 d} \frac{\mu_0 i_1 i_2}{2 \pi x} \cdot d x \\ & =\frac{\mu_0 i_1 i_2}{2 \pi}\left[\log _e x\right]_d^{2 d}=\frac{\mu_0 i_1 i_2}{2 \pi}\left(\log _e 2\right)\end{aligned}$
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