Two long parallel conducting wires carrying currents are separated by a distance ' $x$ '. Work done per unit…
Two long parallel conducting wires carrying currents are separated by a distance ' $x$ '. Work done per unit length in changing the distance between the wires is proportional to
$\frac{1}{\log _{\mathrm{e}} x}$
$\frac{1}{x}$
$\log _e x$
x
Solution
When conducting wire is displaced by $(x) d x$ distance, then work done per unit length is;
$d W=\mathrm{F} / \ell . d x$
or, $\quad d W=\frac{\mu_0 I_1 I_2}{2 \pi x} d x\left[\because \frac{F}{\ell}=\frac{\mu_0 I_1 I_2}{2 \pi x}\right]$
or, $\int d W=\int \frac{\mu_0 I_1 I_2}{2 \pi x} d x$ or, $W=\left(\frac{\mu_0 I_1 I_2}{2 \pi}\right) \log _e x$
or, $W \propto \log _e x$